There isn't really another way to fund Fraunhofer institutes — they're supposed to turn theoretical research into something that can be directly applied ny corporations, so they have to have an incentive to create something like that. With funding through patent fees, exactly this happens.
The alternatives are government funded research, or companies like Google doing it all internally, but then Google will keep some of it as trade secrets, which is also undesirable.
I don't think there's an alternative if your goal is go keep all research publicly available and in a way that any company can easily license it.
But for this model to work, the international community of licensees has to actually believe that your patents have merit.
If you act like a cartel, generate reams of questionably valid patents so that you can hand them out to your member corporations under sweetheart terms and at the expense of your licensees, you're eventually going to piss off enough people to make the music stop.
Evidently, this is what happened. The patent pool is now so large that it's really easy for other players to come in with their own, similar patents. They can use these to create new patent pools and try to take everybody hostage with higher fees (HEVC Advance), or they can build a protective moat and threaten to sue anyone who demands licensing fees from them.
Patent licensing can be made to work in a lot of cases, but these guys really dug their own graves here.
Also, I think there are a number of alternative funding routes that can be made to work. Government funding, as you mentioned, could be one of them. Terms of the funding could stipulate that the research be made publicly available and licensable under reasonable terms.
Companies can also choose to fund the research via Fraunhofer rather than doing it all internally. Not everybody has Google's resources, and there are major advantages to having improvements included in a standard that everybody can access.
The alternatives are government funded research, or companies like Google doing it all internally, but then Google will keep some of it as trade secrets, which is also undesirable.
I don't think there's an alternative if your goal is go keep all research publicly available and in a way that any company can easily license it.