My first solo was stop-taxiback-go too. I don't know if I was specifically cleared to do touch-and-goes later on during my solo period, but I remember doing them solo at some point in time without any objection from my instructor.
What's probably a more relevant question: Once you've gone solo, why would you want to do more touch-and-goes so desperately? You've proven that you can take-off and land, otherwise your instructor wouldn't have sent you solo. I know you've got to fly 10 hours solo somehow and doing touch-and-goes is a nice break from boring holes in the sky but other than that...? It's not like the perfect touch-and-go is an exam requirement.
And there's another trap to fall into. If you do too many touch-and-goes, you might start doing them on auto. Particularly retracting the flaps before adding power. If you ever need to do a go-around, this automatic behaviour can be deadly. In this respect I think go-arounds should be practiced at least as often as touch-and-goes but somehow they weren't when I did my training. I did maybe three go-arounds altogether during that period.