Making cabinet doors w/ windows from plywood?

I was planning to make some cabinet doors out of 3/4" birch plywood
that I have left over. The doors will measure about 22" square and each
will have a window. I was just going to use a saw and/or router to cut
out the hole for the glass, but in my research on cabinet door
building, it seems that everyone builds doors the 'typical' way, which
is building a frame from solid wood planks, then using a wood or glass
panel insert.

Are there any problems in building a door from solid plywood? Perhaps
the frame type construction is popular due to lower weight (due to a
thinner panel or hollow core)? Since my doors will be small, this
shouldn't be an issue. The biggest issue I see is making a perfectly
square cutout to accept the glass, and blending the edges of the hole
in with the surrounding birch veneer (I'd like the edges to be
rounded). Is a router even the best tool to use for this, or would a
jigsaw and a straightedge work well enough?

Also, how deeply can I route the hole, in terms of distance to the
plywood's outside surface, without risking damage to the plywood (from
splintering, etc.)?

Finally, if I use a rounded edge along the perimeter of the hole (when
viewed from the front of the door), can veneer edge tape be used to
cover up the exposed plywood grain? I know edge banding can be curved
lengthwise, but is it as flexible when curved along it's length (e.g.
to cover the length of quarter round moulding)?

If not, I can cut the hole with square edges and glue on strips of
quarter round moulding to the inside edge of the hole.

Thanks