Why were sloths chosen to depict DMV workers?

One reason the scene works so well on repeated viewings is that it's essentially a sketch. The scene is just as funny on its own as it is within the context of the movie, and that's due to its brilliant concept.

Everyone who's ever been to the DMV knows how painful an experience it is. It takes forever, and to those forced to wait for hours, it seems as if the employees are being slow on purpose. Therefore, in a world populated by animals, the famously slow sloths would of course be the sole employees of the DMV.

Refer this for more info.

It's a joke

The actual US DMV (Dept of Motor Vehicles) is renowned (at least in Film & TV) for slow service, long queues and poor efficiency & service.

Now this may not actually be the case but it's a common trope that a visit to the DMV will take a long time.

For an in-universe answer, if I may speculate:

Perhaps in the for-profit sector, sloths are stereotyped as being too slow to get any work done, and so no one hires them. Meanwhile, the city, with its Animal Inclusion Initiative, is willing to hire sloths for desk work where time isn't of the essence. Thus, the sloths tend to find employment in bureaucracies like the DMV; there's no employment opportunities for them elsewhere. Conversely, no one else works at the DMV because they have better opportunities elsewhere (and they may not want to work with sloths, to boot).

After all, the message of the movie may be "Don't engage in stereotyping", but in order to convey that message a lot of the world does engage in that sort of negative behavior so that the characters can fight it.