Can you fire a teacher?

There is a machloket in the Gemara (בבא בתרא כא ע"א) between Rava and Rav Dimi regarding whether you are allowed to fire a teacher when a better teacher comes along. Rava holds that this is forbidden while Rav Dimi not only permits it but appears to require hiring the new teacher.

Rashi explains the machloket as follows: Rava believes that the new teacher will become haughty by the firing of the first and not teach well due to his sense of job security. Rav Dimi holds that the second teacher will try even harder because he will fear that the first teacher will challenge his standing in the community so he will try extra hard to earn a good reputation. Both Amoraim, according to Rashi, are only concerned with the performance of the new teacher but see no intrinsic reason not to fire the first teacher.

The Gemara goes on to explain that even Rava holds that if the first teacher is incompetent, then you may fire him even without warning. The reason Rava gives as to why you may fire the first teacher is that it is 'a loss that can not be returned'. Rashi and Tosefot disagree as to what this means. Rashi holds that the false ideas that were taught and entered the students' heads can never be retrieved. Tosefot argue that the time wasted on teaching the children false ideas can not be returned.

The Shulchan Aruch (יו"ד רמה ס' יח) paskens like Rav Dimi that a teacher may be fired if a better one comes along. The Rambam (שכירות י:ז) seems to pasken like Rava.

The question that arises is whether all this applies to all teachers or only a Torah teacher. It seems that according to Rashi, we would apply this to all teachers since a wrong idea is 'stuck' in the students' heads even if it is not a Torah idea. According to the Tosefot, however, there might not be a din of Bitul Zman when it comes to secular studies.

Any ideas?