In the early 2G GSM days, you would connect via "CSD" (Circuit-Switched Data[0]) which essentially emulated a dial-up connection (except it was digital the whole way) and that was billed per minute. Using HSCSD you could bundle multiple CSD channels for higher bandwidth but the minute charges were per channel so the cost added up.

By the time phones got built-in WAP browsers, GPRS had arrived which was billed per byte, but CSD was still supported (I remember using it once or twice in a certain building at uni where GPRS never worked for some reason)

[0] https://en.wikipedia.org/wiki/Circuit_Switched_Data