Having said that, it would only be acceptable* to me if Congress had similar limits. Moving a term limit for the President further in the extreme direction would increase the imbalance of power.
I suspect that part of the reason that Presidents have been unable to get away with more than two terms (barring one), is a couple reasons...
1) The voters can easier identify a single person as being accountable, and are more prone to actually do so. There does seem to be more critical thought and debate put into who the "top person" is, and less into Congressional offices.
2) The President is not the one bringing home the "pork" to their state/district, which ties back into #1.
*- Key word: acceptable