Adam Funk wrote:

would putting a few coats of this on the
roofing felt every few years be a good way of extending its
durability?

No. The felt fails because the felt itself goes brittle and cracks,
not through the failure of any surface waterproofing layer that could
be restored by painting it.

The main culprit here is UV radiation, so anything you do at
construction time that reduces this can be useful. Sand coated felt, or
even painting it white, will help. Bitumen roofing felt already has
plenty of bitumen in it though, so painting more on doesn't add
anything.

A coat of bitumen paint on the timber underneath is useful though. This
helps to protect the wood from any moisture that does find its way
under.