It does though. Proof (if you want to call it that, I accept it is not formally valid) via contradiction:

There is the immaterial economy which which might theorize can perpetually grow.

There is also the material economy which is rooted in real physics - ie, materials, energy (it will always take some energy to heat up water and prepare food, for instance). Can we rule out that buying metal and building material become completely free? Or that the cost of energy will be reduced to zero? If there is limited supply, there must be some cost and if that cost is too low, someone will buy it up, corner the market, and start charging the correct price.

If so, the material economy cannot grow forever (outside inflation, which is not real economic growth).

If the material economy cannot perpetually grow, but other parts can, then eventually that part of the economy will completely eclipse the non-material economy. As the part that perpetually grows goes to infinitely, the relative value of the part of the economy rooted in physical limits will be worth relatively nothing.

Which contradicts the earlier point part of the economy can perpetually grow when some parts do not, unless the parts which cannot perpetually grow simply become free.