But… shield-weapons as they are now are so much more than push-bashing…
A few push-bashes here and there are super useful and an important part of shield-weapon-ing, but if you feel that that’s their main use, or that it’s all they’re good for, and that their attack patterns are lacking complexity, I’d even go so far as to tell you you’re doing it wrong.
In particular the Sword & Shield and Axe & Shield already have super cool in-depth movesets. Some of their bread & butter combos might boil down to using heavy - light in constant succession, but the real art here is in getting into those combos, and switching between combinations flawlessly on demand during combat. For that, you always need to (instinctively) know which strike is chained after the one you just did.
Some examples of cool combos:
A&S can actually serve decently as horde clear, by chaining the heavy sweep attack with a light attack. You can get there by using light 1 - heavy, or by using heavy after doing a shield bash or a pushattack. Instinctively recognising when you can and need to get into this combo takes some practice, but it’s very rewarding when you find your muscle memory does that almost automatically when you need it. (Same goes for S&S, by the way, and it is more effective than just lights on that weapon as well because of the perfectly horizontal decapitation sweep and better cleave / stagger. Plus it’s wicked fast on S&S.)
With A&S you can use light 2 - heavy and chain that infinitely for single target damage. It’s debateable whether the single target DPS here is better than just light axe strikes, but it is a nice perfectly vertical chop for headshots, and anytime you would normally do the downwards light chop (light3), you can also do the heavy chop. S&S has a similar mechanic where you can chain a light strike with the heavy stab, but pushattack - heavy stab is generally better for single target damage on that weapon. If you are using lights, however, being able to instinctively recognise when the heavy stab is available can be very helpful against mixed hordes, or poking a special that suddenly popped up, or whatever.
(The M/H&S has similar possible combinations, by the way, but most of those are overshadowed by the new pushattack - light combo because it’s so much faster than the rest of the very slow attack speed this weapon has. If the other moves of that weapon are made a little bit faster, however, similar in depth gameplay is also available for it.)
The point is not that these specific combos are specifically great or deep in themselves, but when you have these weapons’ movesets down, the weaving of these combos through your normal shoves and strikes, and the rapidly switching back and forth from them, is absolutely deep and engaging gameplay. I’d even say that these weapons’ movesets are a lot more engaging than those of pretty much every other weapon in the game. You have pushes which are very important to shields, the bash off course, and then all those intricate ways of combining your weapon strikes for different situations. While a lot of (meta) weapons usually have nothing but very similar lights and very similar heavies that all serve a similar purpose, and that’s about it.
And another point: The heavy bash is already very easily available since it’s the first attack after a block cancel. No need to move it to weapon special for availability. And moving it there probably would also mean you can’t affect the time you hold the bash anymore, while timing precisely against a few incoming enemies that come at you is quite valuable for this move sometimes.
In conclusion, there really is no need whatsoever to mess with the movesets of the shield weapons that have the heavy bash. Those movesets are the best part about those weapons, and as per current beta they are in a pretty decent spot balance-wise. Some stat tweaks might be in order, but their movesets need nothing changed. They’re great as they are.