It’s unknown.

It can equally be possible, impossible or not worth it.

Interstellar rocks crashing at you with velocity of 0.1c might hurt a lot.

I would not like my government spending 99% of everybodies income for 100 generations, just to send one human to proxima centauri.

Growth and efficiency gains are not guaranteed, and will eventually stop. (If you take the mass of universe, put it into mc^2, and assume 5% energy consumption increase per year you get 2k years to consume whole universe worth of energy)

We can’t just assume that humans will reach Proxima Centauri.