Analogue sticks for shooters are the worst option anyone could go with.
Straight keyboard is likely to be worse.
That said there is a common variation on the theme of a question to ask when trying to do a task
Is the client happy with the results? This after asking what it is the client wants done as the start of it all.
Does your program output data processed in the manner you wish it processed in a reasonable amount of time on the system you have available to you?
Do analogue sticks allow you to traverse a 3 dimensional world, possibly while detaching your view from the movement*, would the former two be done both reasonably precisely and quickly relative to human reactions and better yet in such a way that the average pleb can do it reasonably easily?
Yes, yes, yes and yes would be the answers to all those. A mouse allows a certain type of camera movement for a certain type of game (the typical first person shooter with weapon axis locked** to camera movement or general movement in the case of certain tanks) to done more quickly and precisely than a conventional analogue stick but an analogue stick is hardly unplayable.
*I will count those that prefer the strafe and vertical look on the same thing and those with prefer strafe-move on the same thing as the more precise version of that phrase would involve axes and other such concepts.
**with a few exceptions, one at the end of this, everything I have ever seen do this has it as an animation quirk rather than any detachment.