In my experience there are two basic approaches to lawns. Both are valid:
- Bag and compost your clippings. In this case, you are removing material from the soil, and so you should also fertilize your lawn to keep the soil healthy.
- Mulch. In this case, you are not removing material from the soil, since the original clipping can return. You may still want other treatments, such as weed, pest, or fungal control, but if you have the right kind of grass for your climate and sun levels you likely won't need to fertilize.
In my experience option 1 tends to nicer looking grass, but option 2 can be overall just as healthy, and it's also a LOT less work.
I personally go mostly option 2, but I also like to leave my first cut of the spring for very late, and let things get kinda shaggy so the roots can get a good start. This means my first couple of cuts are kind of high and the first cut especially leaves a lot of clippings. The result is I need to bag that first cut of the spring.
There's also a point every summer where we're away for a couple weeks, and I usually forget to make lawn arrangements for while we're gone. The circumstances there mean it could be three or even four weeks from the last cut before we go until the first after we're back, and in this case I will also want to bag that one longer cut.
Because I do occasionally bag, I will also fertilize the soil... but only about every third of fourth year. Remember, nitrogen burn is also a thing and we don't want to over-fertilize.
Otherwise, there's one more thing to watch for when mulching: thatch lock. This is generally NOT a problem; a layer of thatch is actually good for your lawn and soil. It helps hold in moisture and block out weeds. But you can also have too much. Thatch lock is when the thatch has become too thick and starts to thin out your grass. In that case you may need to use a garden rake to pull some away. But if you keep up with things, you'll likely never experience this, and if you do it's usually because there's material coming in from somewhere else, as well.