Rashi's expression is based on that of the Gemara in Menachos 42a which says, "If there is no Jewish doctor in town, and the choice whether to ask a Kuti doctor or an Arma'i doctor to perform the Milah, one should prefer the Arma'i..." It is evident from this Gemara that a doctor was the person who would most commonly perform Milah for others. This is also Rashi's basis for explaining the word "Rofei" in Sanhedrin 17b and Bava Basra 21a as referring to a Mohel (and the word "Uman" - normally bloodletter - in Bava Metzia end of 109a also as referring to a Mohel).

Apparently, it was uncommon in the times of the Gemara for anyone other than a doctor (who knows how to apply medicines and to stop bleeding etc.) to become a public Mohel. In fact, the word "Mohel" does not appear anywhere in the Talmud in the context that we use it. Although it does appear in the Midrash in the context of Milah (cf. Bereishis Raba 46:9), there it means "a person who is performing a Milah" (same as the word "ha'Mal" in the Talmud) and not "a person who professionally performs Milah for others."

I don't think any conclusions can be drawn from here as to whether it is preferred for a doctor to perform Milah today rather than a non-doctor.

Best wishes,

Mordecai Kornfeld