Because the Tour of Italy started in Ireland, of course. Sorry. You know what they say about a silly question getting a silly answer.
The most obvious sensible answer is "money".
I believe Yorkshire paid around £3m to get the Tour. This money goes to pay the riders etc. After all, you don't pay to watch like you do for football and so on. Why? Well, it is a Tour and towns and cities (and of course counties) get to show off their delights and tourist potential. Look good to the helicopter folks!
From the interest being shown in the Yorkshire stages (and the difficulty I had finding accommodation a year ago) it was money well invested. Just look how much publicity Yorkshire has received.
From a sort of evangelical aspect, you could say that it spreads the brand cycling and raises its profile. I'll go with that too.
There is a theory - which I will subscribe to - that the Tor de France created the idea of a French nation. We tend to assume that nations go back a long way, but this is not so. In a post-national age, it is politically interesting that events like this are going supra-national.
Spot on with money!
The money Yorkshire paid to host the depart does not go to pay riders, it all goes in a big pot somewhere at ASO. Then the costs come out including prize funds. So you are partially right. Riders get paid contracts by the teams, prize money is an extra and is shared out on a split between riders and team staff.
The TdF started in the early 20th century, and maybe helped to bring the French nation together a little more, but they did have a big sort out in the late 1700's..
What is different - and good - about France (the Hexagon) is that different regions have different food and cultures, but still remain very French. Maybe with the exception of Bretagne and Alsace, where the character is very distinctive, but still French in essence.
2015 the TdF starts in Netherlands, so no Channel Tunnel problems!