Like what obscure robot said, binary is integral to electronics, so naturally 4,8,16 step sequencers are the simplest implementations. If you’re looking for something different, I’d recommend experimenting with modular.
While explicit non-4 step sequencers are rare, there are ways to just make whatever kind of sequencer you want with a collection of modules.
You could create a crazy sequencer with a random gate (think mutable branches), a voltage source (mutable blinds or befaco a*b+c), and some clock divider (I’d go with an nlc divide and conquer). Add some switches and a logic module and you’ll be flying!
If you don’t want to spend the money before trying it out first, take a look at vcv rack. It’s free open source virtual Modular system that has a great collection of modules that you can look into and mess with.
Another idea is getting a traditional sequencer with a reset function and finding interesting divisions and playing around with that.
UI aside (button/knob count), if a sequencer has a reset input or function, it effectively has any step count you like. Of course then you as a user have to pretend the rest don’t exist. However, to limit the actual physical steps makes the sequencer LESS flexible as you’re ruling out other counts.
There would also be a huge minority of possible device sales, if in addition to 3, 5, 7, whatever, the sequencer couldn’t also do 8 or 16.
The Easel has a 5 step. And it’s absolutely wonderful! But I’d be lying if I thought it wouldn’t be more flexible with 8, and then reset on whatever count you want.
Besides that, it’s all in the noggin of the user, provided the flexibility to change length is there.
As others have said, look to modular. Look to voltage addressed sequencers for really crazy stuff.
But really, anything that can reset on a given step is the equivalent of what you want.
Roland MC-4 and MC-202 allow easy non 4/4 stuff.
OP1 endless, tombola, sketch all do too.
Roland SH-101/01a and JX3p all have freeform note entry.
Tenori On has a number of sequencing methods not tied to 4/4.
Older hardware sequencers such as Yamaha QX/QY, Roland various models.
Plus tons of others such as those already mentioned.
They are out there but 4/4, is it is fair to say, is the most widely implemented.
After reading your question and all of the answers here I still don’t understand what exactly you want or are missing with the existing gear and apps available, and what makes Elektron sequencers and alike awkward when used in different time signatures.
The only real limitation with the Elektron style sequencer that I’m aware of would be polyrhythms aside from 3:4 type of stuff. You can remedy this to a great degree by using polymetric patterns combined with the 3/4 seq speed and individual track lengths.
Some ipad apps are pretty good for a truly non 4/4 approach as the GUI can be adapted to any divisions you want but in hardware it would be pretty difficult and complicated if not unrealistic.