Last fall I used my mower to mulch all the leaves in my yard so they'd break down easily. Now that the snow is gone I went out and pushed back the chopped leaves and the soils is really black and moist. Lots of new blades of grass popping up under there.
The question is, should I leave the mulched leaves or rake them up? I'm thinking I should leave them but raking in the spring is a common thing around here.
Also, do you guys rake up the dead grass in the spring or leave it? Do you bother dethatching and aerating?
It depends on how far the decomposition of the leaves has come. I would only rake the bigger leaves up and throw them in the compost bin. Maybe loose up some mats of shredded leaves that have formed. You get new leaves next fall. Dehatching is a brutal method to clear your lawn from organic matter. Wouldn't do that. I prefer raking and adding compost afterwards. That way the organic tuff breaks down by itself. In healthy soil worms do the aerating.
Life that has a meaning wouldn't ask for its meaning. - Theodor W. Adorno
You don't want to cover the grass too much because it will hamper its growth. I ideally look for enough organic matter to where it falls between the blades more than it covers them up entirely whether that's in the form of leaves, blades of grass, manure, or compost.
I used to work landscaping and had to run those dethatching/aerating machines and I wouldn't resort to using them unless maybe I moved in somewhere where the lawn was brutally compacted and abused (even then I would probably rather plant edibles anyway). We would mostly dethatch/aerate to reseed lawns that weren't doing very well and had been under "conventional" care (neglect+mowing with bag+synthetic fertilizers/pesticides).
In this case of the fairly healthy sounding lawn I would make sure the grass can get through the layer of mulch and wait to see what happens. Eventually you could add light layers of compost to your yard and/or some amendments like soybean meal, chicken manure, etc which will continue to nourish your soil food web and do your aerating for you like Dunkelheit mentioned.