Taxiways at low power are unlikely to be much of a problem unless you eat the dust from the guy in front of you. The good news is that most of this dust gets blown into the grass where it sticks
The larger problem is this kind of crap on the runways at the chevron marks. If most of the takeoff for the day power up well downstream of the chevrons and some really heavy guy powers up upstream where the dust has settled than that can suck up into the engine and raise all kinds of problems.
Of course most rolling power-ups help prevent this
There is some data where clogged turbine blade cooling holes can be traced to some specific airports where recent runway work had taken place