Don't know why they release it for developers only and then turn around and allow the public beta just a few hours later. Is there really that high of a demand that they have to be staggered?
It has nothing to do with stress on the download system. It may have to do more with stress on the bug-reporting process.
Each stage of the testing process - internal (alpha), developer beta, public beta, and public release - exposes the software to a substantially larger number of users. A small population is capable of finding major flaws, but you need a larger population, running a far more diverse set of hardware and software configurations, to find the more obscure flaws.
A developer beta is more likely to be a constructive process than a public beta. Developers have a vested interest in seeing the new OS work (and seeing that their apps will run well on the new OS). They'll be far more likely to file bug reports and work constructively with the OS's developers than the public beta testers, who present more of a mixed bag.
While some public beta testers are actively engaged in the test-and-report process, others won't take the time to report - they have other priorities. Filing a useful bug report requires more than a simple, "It broke!" - it means analyzing and attempting to duplicate the issue, collecting logs, and describing it in terms that will be useful to the developer. A fair number of public testers are interested in nothing more than having "inside" access to the next big thing. If they get an onscreen prompt to file an automated crash report, they may just click "Ignore." If the bug doesn't generate an onscreen prompt they may do nothing more than reboot, or publicly complain that the new software is "buggy crap."
And yeah, there's some politics involved. If developers didn't get their hands on the beta before the public, they're less likely to feel like they and the OS developer are on the same team, working together to present quality products to the public. They may feel as if they were thrown to the wolves, rather than have a chance to have a ready response when the public starts filing reports (and complaints). This, in turn, affects the efforts the developers may make to adopt the new technologies and initiatives included in the OS.