The first reason is that I'm quite incapable of absorbing pictures or exhibits for more than two or three hours without suffering from serious information overload.
The second reason is that I need more than one look at a painting. I really appreciated going back to see JayDubya's paintings for a second time at his exhibition in Ashby. See this post from May
Now, I appreciate the Louvre is another ball game, and it's not at all expensive at €11 for a day's entry, but if it were free I would probably have gone in for an hour today, and another hour or two later in the week. And I'd be more inclined to buy merchandise, and overpriced cups of coffee as well.
A compromise - they could make you pay the first time, then allow you up to four more visits within a month. Lots of people wouldn't be in a position to do that, I suppose, but for those who could, it would be wonderful.
To be fair the Louvre and many other museums do offer a free entry day on the first Sunday of each month.