I do think it should be fair to bring up that as of some recent updates which now has updates be handled through the digital storefront instead of the launcher, the issues the Microsoft Store version had were fixed as a result. (This is also the reason Sega advised that those using that version reinstall the game following that update as the location the game's installed to had been changed as a result)
As such... at this point not wanting to take up the Beta purely due to the platform of choice is either some of us being over cautious or just the typical "why not this storefront".
As for why the MS Store exclusivity at all... well other than the fact that Microsoft is the one even financing the release, there's also the fact that the Insider Hub is a very streamlined way of opting into any form of Beta. Of course whether the beta will be a new installation or simply opting participating players into a new patch repository is another story. To play a bit of devil's advocate... while Steam beta features are limited in that the only way to lock out a beta is through a single use password... the Japanese beta did check on login that the account logging in was one of the winning entries... if you weren't then the client would be useless. Arguably, in an ideal setting where we didn't have to account for Microsoft's involvement, Sega could have handled Beta registration through a public survey relying on users' Xbox Live / Steam / Epic account and simply locked out non-winning entries on login.
Now regarding someone bringing up why there's no standalone client... it really isn't an option at this stage as a lot of infrastructures related to logging in and microtransactions are handled through the digital storefront, most likely as a cost-saving measure to exporting the Sega ID infrastructure and system to the West. At this stage, PSO2 is purely dependent on a storefront.
As for the lack of Xbox beta... @Ezodagrom , gave the best potential explanation. Simply put for all we know, this Beta is based on the previous Japanese beta client with some minor fixes and of course, localization files. To my knowledge, JP hasn't even had any console betas yet.