There are some 'firstboot' scripts that need to run to finalise configuration of TKL appliances, but for me they auto run on first SSH login. Regardless I doubt that not doing that would cause that behaviour anyway (as I say I login via SSH to run those scripts...).
The only other thing that I can think of is that perhaps you are suffering this issue (which I personally haven't experienced either) and maybe that is making them unresponsive...?!
I use TKL OVZ containers on ProxmoxVE
And FWIW they all work fine OOTB for me...
There are some 'firstboot' scripts that need to run to finalise configuration of TKL appliances, but for me they auto run on first SSH login. Regardless I doubt that not doing that would cause that behaviour anyway (as I say I login via SSH to run those scripts...).
The only other thing that I can think of is that perhaps you are suffering this issue (which I personally haven't experienced either) and maybe that is making them unresponsive...?!