I leave the mulch on until I'm ready to replant if it lasts that long. It suppresses new weeds and grass growing. If it is still petty thick and in decent shape I rake it off and reuse it somewhere else. If it is pretty much broken down I just turn it under. Having an area covered with mulch until planting time usually makes it easier to get it ready to plant. I do not practice no till. I'm always mixing compost into the soil and rotten or rotting mulch is compost.
I'm sure mulch can give certain pests a place to hide and even overwinter. There is always a downside to anything we do. It's all trade-offs as far as I'm concerned. To me suppressing weeds and especially grass is worth leaving the mulch on during the off season. One possible drawback is that mulch does keep the soil moist. Some stuff should be planted as soon as you can work the soil, green peas for example. For some people that might mean waiting for the ground to thaw. For me it means waiting for the ground to dry out enough. So I usually rake off any mulch that isn't going to be turned under a little before planting time so it can dry out. When I was in Arkansas my windows where the soil was dry enough to work could be pretty tight in spring, especially early spring.
During the growing season one way some diseases like blight spread is that rain drops or sprinkling watering can splash disease spores up on the plants. If you have a layer of mulch during growing season that stops disease from splashing up.