There certainly are reasons for lowering AP's Tx power, most notable being reduction of interference to adjacent APs and their clients. However in OP's case this is not the best solution IMHO. If the problem are clients with low Tx power, then the solution is to reject associations from clients with too weak signal. Those clients will be baffled as they will sense SSID but won't be able to connect and they might complain.
One has to keep in mind that WiFi can have assymetric speeds in UL vs. DL. High APs Tx power enables good DL rates through utilization of higher MCS' that need better signal-to-noise ratio at receiver and higher Tx power helps here. If same client has low power transmitter, then UL will suffer due to reverting to lower MCS for UL. At the same time keep in mind that use of higher MCS not only helps particular client to achieve higher datarates (which that client might or might not need), but also reduces air time needed to transfer data for one client thus freeing air for other clients. Or same client in the opposite direction since WiFi is TDD technology.