Could this sentence be read as having either a positive or negative attitude, depending on the context?

"As a social worker, she gets to go to lots of slum areas."

Can "get to" be modal-like in any of it's uses?
That particular sentence could very, very rarely be seen as positive, simply because "slum" and "slums" are seen as very negative words. When you call an area a slum area, you are not in any way praising it.

Now, as far as "gets to" and "get to," this is kind of a tough area. I think "gets to" is mostly positive and "has to" is mostly negative. "She gets to go to that area" is seen, to me, as a positive statement. "She has to go to that area," depending on context, could be seen as negative.

Generally, to get something is to receive something with permission, so it's usually going to be used in a positive context.

Be aware that in sarcasm, you could use "gets to" and "get to" negatively. If you are being sardonic, then "She gets to go that area" would be appropriate.
Thanks. I agree totally.