It was more exciting to close a door and keep them out than putting on a mask with them standing right in front of you. It isn't suspenseful anymore, so I'm inclined to disagree. Take this comparison for example: making GTA more realistic is a good thought at first too, but when it comes down to gameplay it would be a horrible decision (must brush teeth every morning, take occasional baths, etc.), so making FNAF 2 more defenseless does not correlate to a better game when you remove key factors like suspense (you know they're coming in the office and you can expect it). At some point it stops being scary when you're conditioned to their appearance and repetitive behavior.
In my opinion, the Foxy running animation put the original game on the map. It would be cool if when you're watching the cameras you could be able to see some animatronic peeking at the peripherals of a corner and leaving or seeing some of them run past the open area; them physically moving would be so much creepier than relying on jump scares. The real reason they don't move: low-budget game.
We're meant to believe that they physically move because if they actually teleported then they could all simply teleport into the office and end everything prematurely. Realistically, either they're too cheap or they're broke to enhance the game.
Also, one of many jump scares the game needs to stop relying on. Imagine in the Child's Play films, Chucky was never seen physically moving and only attacked with jump scares. What I'm trying to say is that for stuff like this it's creepier when anthropomorphic designs actually move, when it's clear they're alive and we can see it. This is why I don't find (even though not anthropomorphic) Slenderman not creepy in the slightiest sense. It's just lame; 2014 and games like these are apparently the pinnacle of horror games.
I can't think of any, but I'm not a hardcore expert of the story so that's probably why but everything adds up to me. Except of course the Puppet/Marionette's involvement in the animatronics' creation.