The problem with this approach is how many of us really like the idea of cutting a big check to the govt on April 15? Most of us like to get refunds back (in fact, some people like it so much they think it's a windfall. It's not!). Apart from the illogical need to get money back, unless you've been investing that money during the year, it may be pretty hard to come up with the entire amount on April 15.
Another reason is the April 15 deadline is really only effective if you owe the govt money. If you think you are due a refund, you can file an extension and submit your taxes way after the April 15 deadline. You can still file an extension even if you owe but you are responsible for the interest accrued from the 15th.
IRS FAQ about extension: http://www.irs.gov/faqs/faq/0,,id=199686,00.html