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In most cases we create a noun in -щик from a verb, we observe the following pattern:
носить - носильщик
давить - давильщик
морить - морильщик
красить - красильщик
просить - просильщик
лудить - лудильщик
We have also платить. Why it is платЕльщик then? It seems highly unnatural to me.
This is such called "и - е swap" (мена и - е)
Trubachyov in Труды по этимологии: Слово. История. Культура attributes it to Russian glycolalia (сладкоязычие) which tends to mix stressed й and ль in some dialects.
It is common to replace stressed ий with ей in Russian. That's why we have names like Сергей, Мокей, Алексей (from Сергий, Мокий, Алексий), words like змей, книгочей and the dialectal word Расея.
Glycolalia, among other things, makes stressed иль to be replaced with ель in some words by analogy with ей < ий:
This contamination is most probably the cause of the swap in the word you're mentioning:
Maybe because of платеж / платежный. Maybe if the Russian have платильный not платежный, it would be платИльщик.
