If you are playing a piano, your only option for sound design is to add more harmonics with more notes.
With a monophonic synth you typically have more sound shaping possibilities than on a poly synth. The choice comes down to whether you prefer to do sound design with more notes or more knobs.
This guy is a great resource for people coming to synths from a more traditional background.
+1 for Hydrasynth. I love mine, it is super well built and sounds fantastic. Covers a lot of sonic bases too, it is very versatile. FWIW I’m about to buy a Digitakt which I’ll be pairing with the Hydrasynth and a Roland TR8S. Should be a great setup I hope.
I’d also look at a Novation Peak, another great synth.
I also think the Roland SH4D could be really good paired with a DT or DN as MIDI brain. In other words, ignoring the SH4D sequencer (which from what I read needs a lot of work) and using the SH4D as a 4 part multitimbral synth plus rhythm part all controlled with the Elektron sequencing workflow. Could be the best of all worlds… Roland synth sounds, lots of hands on control via SH4D knobs, Elektron workflow.
I was mainly keying off these statements in the OP
And these in the follow up
Although the A4 is not true polyphonic, it offers something similar and checks off a lot of other things that was mentioned.
Plus it’s small, has a keyboard button situation, and sometimes going for $500-600.
I’d throw in the CV out’s, with 2 audio inputs with nice effects, and the feedback circuitry for long strange generative soundscapes.
In a way you get a little of everything.
Personally I find the 4 voice constraints offer a way to think about creative workarounds which can develop a unique style over time.
To me it offers more with it’s limitations than less.
Depending on if you intend to work entirely out of the digitakt determines if you want a multi-timbral synth.
If you are, then Hydrasynth. Its a wildly versatile synth that sounds really smooth and can easily do what you would want it to do.
If you’re looking for more of a companion, the Access Virus should have the voice potential you would want from a synth to have multiple layers of expansive sounds(note: i don’t have one, but it looks quite deep)
Digitone- limited to 8 voices total, but is perfectly fine. It can be used as a subtractive synth, semi-wavetable, and deep FM possibilities without the need to be a mathematician before designing sounds.
Theres also the OP-1 Field that I’m including in this list of recommendations exclusively as a joke and cannot recommend you go down this route
Appreciate all the replies! So many options here, and quite a lot of synths I’d not previously heard of. Some are crazy pricey for me (appreciate I didn’t specify a price range) but some look like they’re nicely in the sweet spot.
Virus TI 2
On a budget Waldorf Blofeld
I would also recommend Roland sh-4d and add a small midi keyboard. Works really well if you want to perform with it or sample it into Digitakt😊
I think the Digitone is really the perfect companion to the Digitakt, you can cover a ridiculous amount of sonic territory with just those two. And the multitimbrality is extremely useful if you want to make full tracks with that setup, without having to resort to multitrack recording on a computer.
Roland SH-4D
11 OSC Models, 60 poly, 5 part multitimbral, amazing sounds and fx
Also another battery powered groove box so sequence stand alone!
Cant be beat for the price if you want t be able to sequence with more than 1 track on the Digitakt!
There are cases where you prefer a monophonic synth to a poly.
Most obvious case is if you want something for the bass only: polyphony is usually useless (same as a bassist rarely play chords).
Another case is for rich and/or highly modulated sounds. Think of Eurorack for instance, where modulation is everything: every oscillator or modulation you add to the synth gets most likely repeated for each voice, adding to the cost. Plus it might not be relevant musically, as it can quickly become a mess, whereas a single highly modulated sound might still be perfectly OK.
A last thing is that it is IMO way easier to learn synthesis on one voice.
There are cases where a mono shines where the poly doesn’t…
Still, it’s true that while a poly can generally play in monophonic mode, a mono will rarely play chords (some do, in paraphonic mode).
A couple of days ago I bought a PreenFM 3. It’s travelling to my home 
I think it should fit well with the Digitakt.
I didn’t realize it, but this is so true! It’s kinda difficult to program quality poly sounds. High pass, long attack, lots of reverb- beginner pads.
0 sustain, short decay- beginner plucky sounds.
Outside of that. Poly synthesis is more often overkill
I would take something that is easy to program, with most on the controls on the front, to concentrate on learning synthesis.
In this regard, a second hand SH-01a or a JU-06a are good choices.
Thanks for this. You’d take this over the Cobalt/Argon 8? Similar price and, from what I can tell, sound world.
Thanks, everyone. Apparently I’ve run out of “likes” for the next 4 hours (not sure what the rationale of limiting gratitude is) but I’ve tried to like all replies as a basic means of thanks.
Particularly enjoying the mono vs. poly posts. Before this thread, to me, mono vs. poly was sort of like unicycle vs. car. Unless I’m aiming for the circus, those extra three wheels are going to give me so much more potential. But I get it now!
The Digitone might be hard to ignore. Appreciate what some have said re: it being hard to move it away from its very FM sound, and all that that entails, and not being great for pads etc., but when you can pick one up for ~£550 second hand, that’s a lot of sonic loveliness for a very good price.
But the deciding phase continues - not there yet! Got to look into all these mentioned synths. Particularly the Blofeld - that seems a straight up alternative to the Argon/Cobalt I was originally looking at - and the Hydra, which seems almost universally revered (except for this guy).
It is really a matter of personal preference. If you dig a little, you can find love letters to each of those as well as angry screeds denouncing each of them.
Blofeld has been on the market for a long time, so it is fairly easy to find used examples in excellent shape for cheap, particularly if you are patient.
One major disadvantage of the Blofeld is that it’s UI is excellent from a late '90s / early '00s perspective, but Hydra is a true 2020s UI. It lacks the multitimbrality of the Blofeld, but if I was just jumping into synthesis the Hydra would be at the top of my list.
You can’t really go wrong with any of the three, but each will have UI and sonic differences that may matter to you.
I’ve got a Virus and a Blofeld, and the Virus tends to be my go-to polysynth unless I want to do something that is only possible with the Blofeld or that the Blo excels at. A Hydrasynth Desktop is high on my list of synths to buy when I’m done selling my Eurorack. 
One thing I’d add to the interesting posts about that above is that even outside the bass registers mono synths are often adding timbral complexity to the extent that harmonic (or even sometimes melodic) complexity can be overkill for the ear or the mix.
The expressive complexity of the pitch-bend + mod wheel+ legato play style (like Lisa Bella Donna, Daniel Fisher from sweetwater, or that bass station 2 guy on Instagram ( therealfree) is really something to wrap one’s head around coming from a keys background…
The Digitone can sound very analog in my experience, check out my reply to a similar post below. I also don’t agree it’s not good for pads, some of those soundbanks I mention have amazing pads (especially “DigiTales”)!
I had Blofeld, Virus TI, I prefered MM2 (I much prefer filters, UI, size). Now my favorite is Hydrasynth.
I had Digitone, really liked it, I’d also recommend it, but I prefer MM2 and HS for poly stuff. I sold Digitone for Syntakt. ST have 12 tracks, and you can play it polyphonically with a RK002 midi cable.
Really good companion for Digitakt. On a budget, Model Cycle can be interesting too.
@mitya33, still not clear if you want polyphony, multitimbrality, both…