This would open the floodgates to a major proliferation, essentially anything in the PHP API might be wanted.

The side_stats case can currently be done by including the side_stats block, but giving the template no output. But as it loads, it's tempcode will run, so you can load up loads of shift-encoded variables with the values you need.

Otherwise, it is also possible to run PHP inside templates to access the full API (if you turn it on).

Otherwise, you could also write miniblocks and include those in templates.