How do rent freezes encourage building owners to reinvest? They can't raise the rent to recover the cost of any improvements they make. And new buildings would presumably be at risk of becoming rent controlled which reduces or eliminates profits. From my understanding rent controls just encourage maintenance at the lowest possible level.

Neither do high tax rates on businesses encourage (re)investment. They reduce the reward for any given investment. In combination with tax breaks for investment, that does incentivise investment, but that's not the high tax rates doing that.