They have lobbied for a variety of anti-tax payer causes. Namely stuff like: https://psmag.com/h-r-block-and-intuit-are-still-lobbying-to....
There is a really good reason to think that the government would do a better job -- most peoples tax situation is dead simple. Even if H&R block found deductions every once and a while that the IRS didn't -- which I doubt would happen realistically -- H&R block charges something like 200 dollars. It seems incredibly unlikely that they would save more than 200 dollars on average.
And if that was the case, let the market sort it. H&R block could say bring in the returns, and if the IRS messed up we'll find it and split it with you in some fashion.