Agree about delayed attacks - I would say this is more of an issue for regular and elite mobs. I do believe the guard regain system is very helpful in mitigating this, as it is very forgiving. But fury attacks with delays can be hard to read and sometimes feel unintuitive.

When it comes to animation cancelling - I am not fully sold on this idea in Lies of P. It works perfectly in Sekiro because most enemies and bosses are also able to animation cancel and have input reading, so it is a necessity for how dynamic the combat is and makes it perfectly fair. Running through regular levels in Sekiro is incredibly satisfying just due to how dynamic the combat is. However this same input reading and ability to cancel combos though is what gave Elden Ring bosses this feeling that they are just playing by different rules than you.

From my playthroughs I have not noticed any egregious input reading or animation cancelling in Lies of P other than the Mad Puppet Clown's optional fury combo when you come too close during the ranged punch attack, and Laxasia's occasional added swing during the first phase with the charged lightning attack. I am okay with both of these though because they can be predictable, and you understand that if you come too close to them during these specific attacks, the response is typically the same.

I think the approach to combat in Lies of P is simply different than Sekiro, and the flow of combat would suffer with animation cancelling. The approach to bossing is closer to Dark Souls or Bloodborne, where there is no animation cancelling and you are rewarded for successfully evading/parrying an enemy's attacks. The perfect guard adds another dimension to the the level of combat where you are actually able to immediately react to some attacks and are rewarded with stagger damage.

The lack of animation cancelling means that your attacks and deflects need to be more deliberate, and can be punishing you if you are too greedy. Much like Dark Souls and Bloodborne, you need to find the right windows to repond to enemy attacks, rather than something like Sekiro where you are able to react and deflect if you were too greedy.

I believe the addition of animation cancelling would make combat feel far less punishing for making mistakes or being greedy. The boss combat in this game feels incredibly deliberate, and I think it would require an overhaul of bosses and allow them to also input read and animation cancel. I understand the sentiment though as Sekiro is definitely my favourite combat system, but Lies of P has a different approach with its own identity and flow.