Just a thought, a common sense compromise for sane people would be make drunk shooting as serious as drunk driving, if you are caught with a gun while impaired, big fines, no guns for years and multiple or extreme cases means jail.
It appears in most states already it is against the law to be intoxicated while using firearms, and those found guilty of such could face stiff penalties- [criminaldefenselawyer.com]
You're right, no sane or rational individual could object to such an idea as to what you proposed above, the only thing is we haven't exactly remedied the problem with drunk driving let alone intoxicated incidents that involved firearms. Despite some serious penalties such as costly fines and considerable jail time, that hasn't much deterred the repeat offenders among us. A number of years ago had a neighbor who repeatedly got behind the wheel while intoxicated, four times to be exact, and once he rolled his car and nearly killed himself. He must have paid thousands in fines and served time in jail, after the second time, yet that didn't seem to deter his negligent behavior. Sadly, him suffering a fatal heart attack put an end to his poor choices.
So your suggestion is certainly a reasonable one, and rational people could abide by such, but still have my reservations that such measures still wouldn't much deter the truly irresponsible and ignorant among us though, based on some of what I've seen and heard over the years anyways. Some people aren't that bothered by being jailed, or concerned about fines especially if they don't have the money to pay the fines in the first place.