Disagree. In fact its a consequence of control loop theory. A thermostat with NO loss and a finite heat capacity cannot be stabilized.
Its like a power supply with a huge capacitive and (almost) no resistive load. They go unstable as well, because the PSU can supply current, but (not SMUs) cannot drain any.
Yeah, but there's a huge difference between
no loss (would require a perfect iso-thermal environment or infinite insulation), minimal loss (typical circumstances) and a
required particular substantive loss (the case under consideration). The first is an impossibility, the second requires a typical and stable control loop, the control loop for the latter would become unstable if the
required particular substantive loss was missing (by inference, because if the loss isn't
required then the control loop would be unconditionally stable).
As it is, all oven controlled things are bounded by a specified operating temperature range, get too cold and you won't have enough heater power, get too hot and you just don't have cooling, or if you do (e.g. Peltier device) it is limited in capacity too.
You could most likely build a stable control loop in an absolute no loss situation as long as you could ensure no overshoot whatsoever which implies an infinite loop gain-bandwidth product which is as problematic as creating an absolute no loss situation. I'll pass on proving or disproving that speculation, my transfinite maths is non-existent - the very idea of both countable and uncountable infinities makes my head hurt.
Back to practical considerations, my OCXO in its little winter coat is still pulling 132mA @ 5V, so is still losing 655mW to the outside world (less whatever is being delivered as signal power - 5V 10MHz square wave into 5pF CMOS load).