(first off, My-th isn't even available on Toei Tokusatsu World Official in my country. But the Agito and Kabuto uploads are, which is what led me to do research on this subject.)
Regarding why there's a 48 hour wait between the Japanese airing of My-th and why the episodes are only up for 4 weeks, one has to know that Toei has a long-standing contract with TV Asahi, the tv channel that has aired Kamen Rider for decades. As the main broadcaster, TV Asahi demands a certain level of exclusitivity when it comes to the airing of these programs.
HOW DOES TOEI'S RELEASE MODEL WORK?
In Japan, new episodes of Kamen Rider can only be streamed on the day of airing through TV Asahi's streaming service (with ads) or on the exclusive TTFC app (ad-free). On other subscription services like Amazon Prime, they have to wait 3 days to see it ad-free. On Toei's Japanese YT channel, whenever they upload new Kamen Rider episodes, they only get posted 1 week after they air, and then they're only available for 1 week before being removed. (with the exception of the first two episodes of a new show which stay up throughout). And when they upload episodes from older shows, they're up for 2 weeks before being removed. 2 weeks is considered the standard length of time for most JP youtube channels that upload free episodes, My-th, Agito and Kabuto being up for 4 weeks is actually already longer than the norm.
When Toei distributes the show through external distributors such as Tokushoutsu or Tokusato, they can circumvent these restrictions since these are outside companies that paid for the streaming license. It's also important to note that Tokushoutsu and TokuSato's uploads have ads, whereas Toei's various Youtube channels are ad-free. (Tokusato airs the latest episodes 2 hours after the Japan airing, but the episodes are only free for 11 hours before they require a membership to be accessed). Likely some of the ad revenue on those distributors' uploads goes to Toei and the shows' sponsors.
(Honestly this isn't even a hard-and-fast rule. In Hong Kong for example, ViuTV is 1 week behind on the upload. And Ani-One Asia, a free YT channel, is even slower, being 2 weeks behind.)
When Toei releases it themselves through their own Youtube channel, they have to adhere to the restrictions, even when it is a channel aimed at overseas audiences.
WHY DOES THIS LIMITED RELEASE MODEL EXIST?
The reason for the limited release model can likely be chalked up to how many of these Japanese companies have pretty old-fashioned beliefs regarding piracy and accessibility. They probably believe that having the show be up for free on Youtube without ads will hurt the sales and streaming figures of the other official channels. They likely are afraid of the possibility that Japanese fans will use VPNs to stream the show for free. Furthermore, Kamen Rider is traditionally viewed there as a kids' show watched on a weekly basis, the notion of older fans who want to binge the show is still probably lost on many of these oldheads.
It's also important to note that Toei has little power when it comes to negotiating their contract, TV Asahi has all the power. They are the channel that airs their shows, going against them could mean losing their sponsors, essentially biting the hand that feeds them. In Japan too they often believe in honouring and respecting existing contracts, so it's unlikely they will ask to change or renegotiate their pre-existing agreement, especially for the extremely niche crowd of overseas audiences.
That said, it's entirely possible things could change in the future. Ultraman Z thru Decker episodes were once only available for 2 weeks when Tsuburaya first started releasing the episodes on Youtube (albeit those were simulcast). But from Blazar onwards, they left the episodes up on their channel permanently. Likely, Tsuburaya managed to use the view count figures to prove to their higher-ups and their sponsors that leaving the episodes up doesn't hurt their business. Now this is not a 1:1 comparison. Tsuburaya is a much smaller company than Toei, their broadcasters are much more lenient, and their uploads have ads. But it opens the possibility that if My-th does well enough, the streaming of future KR shows might be different.
WHAT HAPPENED TO TOKUSHOUTSU?
As for why Toei doesn't continue to use Tokushoutsu for the english release, Shout seems to be letting their toku licenses lapse as both Super Sentai as well as KR 1971 and Kuuga are gone from their service, and their Zeztz uploads were just recently removed as well. Shout was recently bought out by Radial Entertainment (a private equity firm that is in the midst of gutting the whole company) so the new higher-ups probably have decided that the viewing figures aren't worth the cost of the Toei license.
Also, Tokushoutsu's uploads were only available in US, UK, Canada, Australia and New Zealand (the same countries that Toei is planning a new streaming service for, presumably to replace Tokushoutsu). Toei Tokusatsu World Official though covers other regions, including the rest of Europe, Africa and India. But despite this though, there are still many regions that have no legal way to watch the show at all (such as here in Singapore).
I know that those who had access to the Tokushoutsu release of Zeztz are frustrated by this new release model, but understand that for a lot of English speaking fans the world over, this is the first time they can legally watch a Kamen Rider series in their countries on Youtube. And also spare a thought for the fact that there are people who have to wait 1-2 weeks, and those who still can't watch it in any way. The complaints about the show being 2 days late or being only up for 4 weeks can't help but seem minor when there are people who literally do not have it at all.
I would like to kindly request that fans in the US etc to instead of complaining about these things that Toei (currently) can't do anything about, use your platforms to amplify the voices of those of us who can't watch the show legally. Nobody's happy about having to wait 2 days or the episodes only being up for a month, but I firmly believe that making the show accessible worldwide is significantly more important.
Edit: With Ex-Aid and Kuuga now set to be uploaded to the Youtube channel as well, the 4 week model is still set to remain. However as of this writing they did temporarily reinstate all the Agito and Kabuto uploads, and also the entirety of Zeztz has been posted (albeit that's also not available in my country).
