It depends on the amount of instructions which have to be executed. Every keyword has to pass the interpreter using any kind of Basic. The more keywords are used the slower will be program execution.
Regardless of the number of instructions, interpreted BASIC is far slower than compiled code.
Also the memory space in MICROCHIPs as well as in ATMELs is very limited and won't allow to use a basic interpreter, which I guess would be appreciated by many people.
Where have you been the last 20 years?, the BASIC Stamp is a PIC interpreter, and the more modern PICAXE is another one.
There have also been two free amateur PIC interpreters based on the Stamp, neither ever reached fruition, but were workable - a bit like the forerunner of the early PICAXE, stored the program in internal data EEPROM.