higher transmit powers do improve range when you have a good wifi radio on the router which is sensitive enough to work with very weak signals.
Also wifi connect rate is not uniform, the upload rate and download rate are determined separately so higher transmit powers can improve download throughput even if the range is not improved due to a client transmit power limitation.
Over the past few years transmit powers have increased significantly even though very few router companies do not advertise the transmit power.
from the days of the wrt54g's it was common to see 15-30mw transmit power, but today, your average/ mid range router will have a transmit power of 600mw, and some of the higher end ones, eg look at the fccid's of a few netgear routers (they don't advertise their transmit power on their site but they are pretty high), you will see around 600-700mw on their mid-upper mid range routers, and around 900-1000mw (the legal limit set by the FCC) for their high end routers.
Most users focus on download speeds more than upload (and confirmation packets take very little bandwidth). By boosting the transmit power, you can not only ensure that any range limitation in your network is is due to the client and not the router, but for what ever range you have, on average, you will have higher download speeds.