Isn't usually the bride side of the family that pays for the wedding? Or has that gone by the wayside?
That has mostly gone by the wayside, but even if that were still the norm it doesn't change the OP's post and the responses.
The OP (bride's parents) are willing to foot the bill. They just can't afford the type of wedding the bride wants. If the bride wants something more elaborate than what her parents are able or willing to spend, she will have to come up with the rest of the money.
I think the tradition of brides parents paying for weddings made more sense when women were getting married at a young age. Parents now, like the OP, are paying tens of thousands of dollars for their daughters' educations and often helping them out financially during their young adult years. The money that parents may have saved to pay for a wedding is now going toward these other expenses. It's a bit ridiculous to expect that a bride's parents should be obligated to pay for her wedding when they may have already spent $100,000 on her education.