Depends on how many leaves we're talking about!

In my backyard, that strategy works great. In my front yard, there are
so many leaves that even if I ran the mulching mower over and over
again, I'd still have a layer so thick it would suppress the grass.

Exactly, if there is a lot of leaves, mulching alone will still leave
a layer of mulch leaves on the grass; they just cannot decompose fast
enough -- not good. I will use my mower to "bag" the leaves. My Honda
mower will mulch the leaves to small pieces despite the fact that I
set it up for bagging not mulching. Then, I dump the whole bag of
mulched leaves into my compost pipes. I will mulch agin (instead of
bagging) if there is only small amount of leaves or if I am mowing the
lawn.

Moreover, using a self-propelled lawn mower is MUCH easier than using
a leaves-rack. I would much rather to get my exercises through other
means.

I remember my old JD lawn mower cannot cut the leaves into small
pieces if I use it in bagging mode. Somehow my Honda can do this in
bagging mode. This must have to do with the fact that the Honda lawn
mower has 4 cutting blades instead of just two.

In the front yard I use a leaf vac - a big one that looks like a lawn
mower from a distance. The bag holds almost 2 cubic feet of shredded
leaves, and I'll get two bag-fulls twice a week from less than 400 sq ft
of lawn. No way I could leave that much on the lawn! I dump about half
of it on my vegetable garden, toss some manure on it, cover it with a
tarp, and till it all in come spring.

I also have a leaf-vac. Unfortunately, it is not a self-propelled
version, and pushing (actually is pulling) a leaf-vac over the lawn is
not easy. Therefore, I stick with using the self-propelled lawn mower
to bag the leaves from the lawn (this also can cut the leaves into
small pieces). Now, I only use the leaf-vac on flat surface, such as
the drive way and the curb. I might have used the lawn mower to take
care of leaves on flat surface in the future; but the leaf-vac "seems"
to do a better job in sucking leaves from flat surface, and I can use
it to shred fallen tree branches along the way. When the leaf vac
dies, I may use the lawn mower to take care of everything.

If you have a self-propelled leaf vac, you will have the best of both
worlds.

Jay Chan