The IT point of view is going to be that a a standard package load out reduces testing requirements for applications, patches and drivers, provides for a spare parts inventory, and allows for volume pricing to reduce total cost of ownership. It also allows for standardized documentation that can be handed down to lower level technicians. Ultimately IT is a cost center in many organizations and have continually constricted budgets so things increasing ongoing costs are seen as a no-go.
When you open up a BYO program you now have to provide for a variety of configurations, customizations, and drivers that will require debugging. I ran into an issue where my Microsoft Surfacebook conflicted with my 5GHz wifi, causing reduced speeds. I fixed it with a registry edit changing driver settings, but this is now asking your local IT team to figure this out and fix it x2000 employee configurations It increases the time to repair on all systems. If a part breaks, how do you repair it? Does the employee handle the repair process or the company? What security do you enforce on the BYO configurations to manage your data requirements? Now the IT team isn't the only team involved, it also needs Security, and probably 3 or 4 levels of management.
Suppose you take a step back from a full BYO program and just offer an expanded selection. Instead of the 15" Dell Laptop, you can now get any Dell business laptop, and have a choice of Win 7 or Win 10. This is more manageable, will still allow for volume discounts. However, it increases the testing and documentation demands, in particular with in-house applications. Some of this is done anyway as a part of full scale operating system upgrades, but why do this early? There's other projects and things going on, and the operating system team on IT has their own timeline for testing and vetting internal applications. If you have 2000 developers you probably have just as many sales, marketing, accounting, and other support positions, each with their own applications. If you don't do a full rollout company-wide, a question that might be asked is why are developers special enough to justify this treatment when it's good enough for 2000 people? No other complaints have been heard.
Opening up to even more operating systems, like OSX implement additional cost and complexity. Adding Linux involves an entirely new skillset that generally costs more than experienced Windows administrators. You also need to feed those skills and documentation back down to level 1 & 2 who are going to be doing the hands-on repairs and issues like connecting to projectors and wifi.
Changing an IT process like this is going to involve multiple levels of management to justify the budget for increased support and changes in process. It's not something you can ask even the first line managers for, so I hope you're prepared for the bureaucracy this will entail going through. It is doable, IT as an industry is being more accepting of mobile devices and multiple device configurations. It requires alignment between internal app developers and IT to support these applications, as well as migrating off old apps that may require specific combinations, and then diligence with testing and deployment.