In fact this is exactly the case with anyone working directly for the federal government, doing research or otherwise. You're told in no uncertain terms that at any moment information on your work laptop can be FOIA'd in which case you will have to immediately hand over the contents of your hard drive (if it has been determined there is a reasonable likelihood that it contains the FOIA'd information). Obviously if you're working on classified state secrets the process is different (also personal information is redacted from the documents). There's no reason research can't be accomplished successfully given the condition that the public has a right to that information at any given moment.
Academia can be extremely competitive. Like, if a competing lab got ahold even of the title of your upcoming paper, they would and do rush to duplicate your results, and try to publish before you to get the scoop.
For that reason, I don't know if open access to everyone's hard drives would work.
Nobody gets to "own" an idea. This possessiveness and reputational greed is what is causing all of these problems.
They should be allowed to make copies of it (in which case it isn't theft). They should not be allowed to deprive you of your copies of the information.
Second, the taxpayers did fund your research (assuming you research at a university), even if you had to work for that funding, and the results should be publicly available as default. Or can you provide a reason for why it shouldn't?
Personally, I'm biased even without the taxpayer argument since I believe in online learning (duolingo, OCW, etc.). I also know most published papers will only be skimmed at some later date by people highly involved in that field, and so having the information available to interested taxpayers doesn't seem to me to be an issue.
What is your field? And why don't the members of this field just create their own on-line publishing venue?