It does, but commercial property tends to change ownership and undergo construction more often. Therefore property taxes on commercial property tends to be higher.
As a result, cities have an incentive to build commercial property over residential homes. The result is that the people working in those offices are competing for limited residential space (leading to high prices) and often have to settle for long commutes (leading to gridlock).
Prop. 13 means that a commercial renter can rent out the land to one tenant after another virtually forever without the taxes going up very much at all (way below inflation). At some point it gets to a point where it is never economically advantageous for either renter or landlord to ever have the landlord sell... the situation is only disadvantageous for the city/community (which is getting far less in taxes than other places).
Even if commercial property is changing hands, there are well-known loopholes to structure that as multiple transactions, none of which transfer more than a 50% stake, and which therefore do not trigger a Prop 13 Reassessment.