*warning: amateur*

I am beginning to get serious with my gardening, and trying out new
things. I grow using 4x4 raised beds, and was thinking that maybe the
pathways are a useful way of converting weeds and the ash of fireplaces
into a useful soil again?
By this, I mean that instead of walking on plain subsoil, as I've
been doing (I am too lazy to pave, and like to scrape the path every now
and then to add to the plots), I am considering lining the paths with
fireplace ash, in an effort to reduce garbage costs - the ash would be
walked into the subsoil, eventually mixing with it to form a clay. I'm
in a moderately wet zone (Ireland), so this should not take long.
After a few weeks of doing this, I figured that instead of burning
weeds (what a waste of good nutrients!), I could do the same - just toss
them on top of the ash, and walk them into the subsoil. I figure that
the weeds would find it difficult to take root in the subsoil, and the
ash would smother them, and after a year of being walked on, their
ability to propogate would be weakened severely enough to allow the
resultant clay/organic mix to be used as a small top-up to my plots.

Has this been tried before, and with what success?

A friend of mine said he'd tried that a few years ago, but was warned
not to be some more experienced gardeners - when I asked, he couldn't
tell me whether it was through their own experience of trying it, or
because of "common wisdom" (or "because that's the way it's bloody done,
that's why", as I prefer to think it).

Any thoughts? Any reasons why this would not work? Any reasons why I
shouldn't even bother trying?

Kae