Have had quite a few jobs with mesh over, it is a pain in the bum, what happens is the gutter 90% ish run free water will go where it is meant to in the drain, what people see is overflow of trees muck ect hence why they want them cleaned, mesh work most of the time, removal of it will make it worse IMO.
I have been doing gutters for years now, the worst ones IMO is the matting (I cant see the point of it gets wet sags and muck builds on top yet still companies sell the stuff (rip off IMO)
Ian