small puncture tire repair

I wonder if some tire pattern attracts more nails than others.

I have used tire patching kits before -- the kind that requires you to make
the tire puncture hole larger first with a file, and then push in a rubber
plug, then pull out the plug insertion tool. Some requires glue, and some
comes with sticky plugs.

Anyway, among the tire patching kits, is there some that doesn't need to
make the puncture hole larger? I hate to make the hole 5 times bigger just
to repair it.

For small puncture hole, is it possible to simply inject some glue into the
hole to patch it? Perhaps some sort of expanding glue that remains flexible
when cured.