You never need to remove mulch - and it doesn't matter what kind you use as long as it is an organic or degradable mulch. You just want to avoid piling it up too deeply.

I apply the mulch 4-inches deep to reduce weeds. (In fact, since In May 2015, my garden has been weed-free (smiley face)!

In February 2018, I raked the mulch away from my roses, applied Milorganite then raked the mulch back into place.

Yesterday (April 8, 2018), some weeds had sprouted from the soil so, apparently, the mulch is too thin around my roses.

I wouldn't bother incorporating the old into the soil. Let the soil food web take care of that. Just add new on top.

I agree. Why make work? Just put the new mulch on top of the old and leave it be.