Simple math of increasing skill after scenario:
1. Successful skill check on scenario = chance to improve.
2. Roll to improve = Roll d100 above skill, or above 95 if skill is already 96+, to get 1d10 increase.
Stats-wise, for someone with a skill@100, they'll have a 1/20 chance of getting an average of 5.5 points.
Meaning the skill should be at about 106 after they repeatedly braved a CoC-situation for 20 times. (As it's CoC, probably not that many investigators can live that long.)
This is not definite, of course. In fact it should be far less likely they'll get any increase after 20 advetures, as it is a 5% chance every single time.
But just assume they are that lucky.
106>111>117>122>128>133>139>144>150
x+20>+40>+60>+80>+100>+120>+140>+160>+180
The investigators would have been through this 180 times by the time they've made 150 skill. (Not including all the things they went through before they reached 100.)
They've also probably physically beaten Cthulhu to a pulp over a dozen times that it's gone full-blown insomniac and seeing psychiatrist regularly, and had a house in Ry'leh since they practically live there anyhow.
Either that, or the player really have the luck pf a harem-protagonist (And a real life harem maybe... Nah, 24/7 domestic dispute ain't so lucky I guess. v=3=v)
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Still, if your GM lets you put all the points in a skill or give you 30000 points to start with, then I don't see why not. Go for it.
Just don't try to convince me that's perfectly reasonable in every game. It ain't.
At least have the guts to stick up for playing however you want, don't hide behind the excuse of "everybody's doing it".