I mean paper doesn't have to be inefficient, in fact it rarely is since paper based workflows are often optimized. Everybody working with paper understands the process and can therefore come up with ways to optimize it.
I once worked at a hospital which had paper files. It makes sense since the documents in there can be in a lot of different types. The process of dealing with it was rather efficient on the paper side, you had some numbers and got the file with that number from a cabinet. The actual bottleneck was the computer based indexing system. We had something similar to E-Mail called "Outlook/Exchange". We ended up printing out those pseudo E-Mails, looking up each number individually in the indexing system, and writing the number of the file next to it. There was no way of sorting the entries to be able to reach them efficiently, nor was the system well designed. (it had SQL injection bugs!)
This is just one example of how badly designed computer based workflows can be.
Then there is the other point of governments being supposedly less efficient than companies. I have no idea where that idea comes from. I have 2 retirement funds, one run by a private company, the other one run by the government. While the government one manages to pay out millions of pensions every month and flawlessly adapts to any changes in my life, the private one can't even get a simple address change right, twice in a row!
Why should companies change? Companies mainly act to self-preserve. Any change is not just constructive, but also destructive. For a company to change it would need to have a vital reason, without that reason it cannot change.
Some people claim that there is the magic hand of the market which will somehow fix the problem though something called "competition". Those people go on citing exotic areas where their dogma actually worked and there was competition. However look around you. Go to an electronics store with a list of brands that come from the same manufacturer and then look at how many different prices exactly the same product gets sold. If there was competition, everyone would buy the cheapest of the otherwise identical products. There is no competition on many markets.