That is Hollywood, not reality. Tossing happy drunks into cells to sober up overnight is not a thing.
(1) There are no happy drunks. The drunks cops arrest are loud and aggressive. Often the physical act of arresting them results in more violent behavior.
(2) "Drunk" is not a thing for cops. They don't know if the person has had too many beers or had just taken LSD, or both. If they assume a person is simply drunk, and that person dies in the cell of an overdose, the cops will be responsible because they isolated that person. Cops are forced to treat intoxicated persons is more like patients than a 'drunks'.
(3) Mental health problems can look like, or at least exacerbate, intoxication. Cops cannot casually lock people up under the assumption they are dunk when in all likelihood they may be a non-drunk person in the middle of an episode. So cops must test people, evaluate them to determine what is at play. That takes time/money.
(4) Police cells are not happy places. They aren't private 8x4s with a soft cot. Spend a night in an LA lockup. You will not be getting much sleep. Casually throwing hundreds of drunk people into that mix will not help.
Assuming this is just about happy drunks, businesses that get people drunk and let them loose on the streets share the responsibility. We cannot allow bars and liquor stores, and their patrons, to rely on a pleasant police force ready to keep drunk people safe after the bar closes. If a bar is going to serve someone to the point of arrest-worthy intoxication they must contribute to the cost of keeping that person safe.
I saw a BBC doc yesterday about drinking in the UK. They have stores selling 3-liter bottles of 7.5% cider for four dollars. That is ridiculous. 3-liter bottles of dirt-cheap alcohol, cheaper than coke, are not bought by happy social drinkers. Any store selling those knows what it is doing.