The only thing I do not like with fixed camera angles is . . . for lack of a better term: getting lost. With the likes of games like DMC and LOI, the perspective can change quite often and you can find yourself becoming disorientated, i.e. not too sure which way to go in relation to the preceeding camera angle(s). Hence, you sometimes find yourself moving BACK into the previous area. It can be frustrating. I remember the original Devil May Cry and its opening hall: it was a nightmare trying to get the lay of the place initially. Devil May Cry 4: there was one bit where you quick jump (cannot remember the technical term) across a ceiling but you have to time it. When you reach the other end the camera looks back the way you've come: initially, you're not sure if you have more jumps to make, or if you've reached where you need to be. I swear I've jumped back across to where I started because of the bloody camera angles.
Another potential issue lies in the analogue stick for movement: if you're holding down to move into a room, let's say the fixed camera changes to a different angle: your down movement usually continues in perspective, so the character could now be moving right onscreen, but you're still holding down. If you release the analogue and stop the character, to continue, you need to move right on the analogue stick. It can be jarring. DMC4 definitely had those issues: you had to basically release the analogue and re-go from the next perspective.
But there are always going to be little issues like this, whatever method . . .