You don't even need to make it complicated and walled-garden with eFile, just have the program end up with a printable PDF that you mail to the IRS.
Want to incentivize the IRS to open their eFiling system so someone like the FSF can eFile or make their own ? Just send 10,20,30m paper 1040 forms. That will quickly cause the IRS to want alternatives. This will never work for a simple reason.
The problem, as I see it, is that people misunderstand what value online eFilers offer their customers.
I could have gone on TurboTax website the day I got my W-2, filled out their forms and "get your money in as little as 1 minute," deposited directly into their bank account where you get a virtual debit card. Regardless of your opinions about that scheme, many people are very attracted to it and in my hypothetical paper filing logjam scenario it might take 6 months and legislation to resolve it, nobody wants to wait for their refund, not even for the week or two it takes the IRSs normal ACH, I want it in 1 minute! This is (part of) the real perceived value from companies like TurboTax. Is the FSF going to fund advances like this? Of course not.
The other half of the value proposition from them is protection against mistakes. Again, regardless of the actual utility of these claims, some people are very afraid of making seemingly minor errors on their tax return and being faced with a huge tax bill with huge fees and fines and penalties. Yes, I know that the IRS is actually a semi-reasonable organization and for the average filer the chances of having something like this happen is effectively nil, but, people are attracted to the security of those protection guarantees. Is the FSF going to back their software with a similar liability promise?