I agree there is something perverse about wealthy criminals being given free bed and board at the taxpayer's expense. It's known for some wealthy career criminals to see prison as a "temporary inconvenience". However, I expect both of those are a minority of the prison population, and many prisoners are there because crime is the only way they know of making a living.
A far bigger problem than who pays for prison is drugs: drugs fuel crime, both inside and outside prison. It's extremely easy for drugs to be smuggled in, prisoners often leave more dependent on drugs at the end of their sentence than at the beginning. It's known for dealers to make more money in prison than they do on the outside. It's also very difficult to prosecute those at the very top of drug gangs, because "Mr Big" never gets his hands dirty: his mules and sellers are the ones who end up in prison. Perhaps we need a special sentence for "leading a drugs gang: prison, and confiscation of all assets".
The problem is that prison is the only punishment we have for people we don't know what else to do with, such as prolific shoplifters, tax avoiders, those who commit crime as soon as they leave prison, so they are then guaranteed a bed and three meals a day.
I think there is something to be said for fines being calculated according to income, as they are in Finland. We hear of footballers and bankers paying a measly £500 for speeding at 150 miles an hour, when they should be paying something for which they have to sell their Ferraris. (Small contribution to the prison system!)
And more needs to be done about the law, and sentencing guidelines, so that we don't get so many lenient or non-existent sentences. There are some people who should be serving long prison sentences, such as hit and run drivers who kill (see other thread), and the cyclist who killed a pedestrian (on the pavement) and walked away from court with a fine less than the value of his bike.