Another point of view to consider…
Depending on your antennas it can be difficult to perform antenna tilting. If you do not have remote tilting on your antenna (even just remoted to the base of your cell site tower or base station equipment room) and you need to get an elevated platform/crane/cherry picker to the site to make the change, it can be expensive to do so. Motorised remote tilt makes such optimisation manipulations much easier (very important in a WCDMA or CDMA based network). You may if a situation is bad enough consider down powering a site as a short term measure until the antenna tilt can be changed – but typically that is only for short term situations.
Having said that, I still would not advocate for power reduction as an optimisation technique unless it was last resort.
Indeed there are instances where overshoot may be acceptable, particularly if you have to tollerate it to achieve your coverage objectives – but it is a careful tradeoff between how much overshoot to tolerate verses overall network performance. A balance needs to be struck and only sites covering areas where no other coverage can really be achieved any other way should be considered for up-tilting and hence acceptance of overshoot situations. If you are running a GSM network, it may be possible to work around an overshooting cell through careful frequency planning – leaving the cell it overshoots as an embedded cell operating on a different frequency. If it is a CDMA based network then that option most likely doesnt exist.