The GNU AGPL doesn't make sense for most programs you use (programs installed
on your own computer); if it isn't commonly run over a network, and very few
free programs are, the AGPL's additions do no good. That would be mainly why
so few programs use it. But some very important software does use it. Ryzom
is one example, and so is MediaGoblin. It's just that the amount of important
free software that the AGPL is the best choice for is small. It's important
to note that SaaS is extremely rare; the usual practice is to send a program
(usually in Javascript) to the user's computer, where it is then executed
locally on his/her browser.
If you hold the copyright, you can put whatever license you want on it. Of
course, if you release it under a permissive license first, that code will
always be available under that permissive license, so switching to the AGPL
will not affect that code (and it might even cause some disgruntled users to
fork it, if it's popular enough). But for example, licensing it under the
AGPL and then later on offering the dual-licensing model you describe would
be fine, since you were planning on using the AGPL anyway.
As an aside, there's no sense in refusing to offer paid support to users
using the AGPL with your program. Just charge for the support and make some
extra money if people choose to take advantage of it.