Installed on 3 systems and counting. The installer hangs sometimes. I try again later and it's fine, as you found out.
If there were any limitation on the number of installations per user ID, it would be so easily circumvented as to be pointless. All someone would need to do would be to create another BandLab account with another email address.
They're giving it away for free, they want everyone to use it and eventually, I presume, when more BandLab integration features are in place, use them. Or when we get exposed to the new users who need help in the (soon, please, soon) new forum, we can help them find their way around.