except you can only do it on one of your attacks on each turn.
Yes, and if you have access to different types of attacks, and miss with one of them, you get to use it on the other should you hit with it.
I think the main problem with Sneak Attack applying passively with multiple attacks is when you have multiple targets, sometimes you don't want to waste your Sneak Attack on your first attack.
E.g. you're engaged by a low-hp enemy that you just want to finish with a normal attack, and then move 20 ft to sneak attack a full hp enemy.
This isn't a big problem in the EA, but will become more significant with more levels and multi-class. Basically, as you get more attacks to spread out, and your sneak attack bonus gets higher, it's going to suck not being able to control when you can activate it. For example, based on BG3's implementation of the Thief, a Fighter 5 / Thief X can have 5 attacks (haste + dual wield), so that's an element of strategy removed if your first hit is always forced to be the sneak attack.
For what it's worth, I do like the toggle solution that mrfjui3 and CJMPinger are putting together.