Actually, it looks like only one major browser company, Microsoft, has a philosophical problem with supporting multiple codecs
, because apparently they are concerned about the poor customer getting tied up by intellectual property rights!
So yes, you have a quandry; you have to predict the future of that browser.
But for now, if you want to support all
the major browsers, you have to serve the video in multiple codecs, or provide both html5 and flash (as youtube does), or do flash only, or use a third party host who does one of these for you, or put up an annoying message saying 'please upgrade your browser'.