Though it seems like internal IT still has to handle a lot of it. So, I really don't understand why they do it.
Salesmanship, and the fact that it is generally a good deal for business. Dell's contract and negotiation teams earn their keep, I can tell you that much, they know exactly how to present the variable costs and risks of self inventory against the fixed costs of "we'll handle all that and just give you machines and take back bad ones". Having your local IT be reduced to handling machine assignment, RMA's, and software issues that can be fixed on site means fixed, predictable costs for the business. Computers are an overhead, not a goal, they just want them to work. Having a guy who can run weird frankenlaptops is great until that guy gets a better offer, and then your entire fleet is fucked. Same with the relative manpower spent on individual deal hunts and small batch acquisitions. The stuff internal IT deals with becomes more the inventory and asset management side of things, making sure you know who has a given laptop, that you get it back when they're gone, that you have spares in your various manned locations in case of failures, that the appropriate bios updates are applied to inventoried machines that aren't deployed, etc. All stuff that isn't realistic for Dell to manage for you anyway.
The contract 'bloat' is also often not even seen as bloat, but as better than the alternative. If the dell contract introduces a $10,000 overhead, but corporate accounting considers manpower to be 'worth' $100/hr for internal accounting, then anything that takes more than a couple weeks for one dude to deal with is worth less than spending that time somewhere else. Its also why there's basically no point to in house repairs, the laptops are a few hundred dollars a unit, and anything more complicated than trivial maintenance is quickly not worth the cost. Some places might have a value closer to $50/hr for the deskside team, but those ballpark "I fucking wish I got paid that much" numbers are the lifeblood of higher echelon decision making.
A lot of gaming studios use Dells for the dev machines.
Gaming studios, specifically the people who actually need better than a dell like the Artists and some (not all) of the programming team makes up a fraction of a fraction of the addressable market. And even inside EA and the other players out there, a significant number of their machines are still just running basic software. Managers and project leads, leadership and HR, Finance and Marketing, None of them need much more than a mid grade Latitude. The actual 'high spec' users are the exceptions, and it once again works 'well enough' for their needs. Who cares if the things gonna scream to death and cook itself in two years, put on some headphones when baking the lightmap, and swap it for a ready unit that we'll just reimage your shit onto from the cloud backups and get back to work, we will RMA the fried one.
Think it was all just $$$. Getting a big replacement contract was more desireable than meagre 'maintain our shit' and Dell is a recognizable name. Budget-approval friendly
Budget approval is a big element, when you're asking big bucks instead of trickling out a few machine buys here and there, you end up with director and VP levels involved, not the 'normal' finance penny pinchers that'd flag IT for weird and irregular spending, which they fucking hate. And sales people know how to convince executives on the merits of fixed costs, even if they're higher. Its easier to budget for "We'll definitely spend $80,000" than "Well we might spend $80,000, but we might also only spend $40,000, but its possibly we go up to $100,000 if we lose the silicon lottery this year". Asking for money and not spending it is a great way to get fucked in corporate finance, because if you do get approved for $80k and then only end up spending $40k through a combination of luck and good hardware maintenance, then great - next year your hardware budget is $40,000, because you proved you can operate at that level. Good luck, fucko, your miracle performance is now the expectation, because you are an overhead and not a revenue generator, and so taking that $40k and giving it to the guys who actually make the money was always the goal.