I know a fair bit about Psyspam and what it's capable of; if I wasn't the first one to come up with Deo-A + Lele back in January, I was definately the first one to post a rain psyspam team:
http://www.smogon.com/forums/threads/doubles-ou-team-bazaar-sample-teams-here.3590987/#post-7166026
I basically came up with the idea for "BrainStorm," as I called it, while I was battling Lolk who was using Lele and rain. I realized that Lele blocking priority was a huge win for rain teams, which used to be plagued by stuff like Thundurus's Thunder Waves and strong priority attackers. Then I thought "hey, Deo-A also benefits from this, and Psycho Boost would probably be really strong."
The golden age for this build was probably in early January during the np: DOU Stage 0 era. Magearna and Zygarde-Complete had just been banned. People still thought Tapu Fini was the worst Tapu (lol) and quite a few people were hyping up Lele or saying it was broken. Nobody was yet adapting to or considering Deo-A an implication to their teambuilding. Yes, it took an L to Trick Room, Ferrothorn, and sometimes Jirachi, but for a while bringing this team basically meant risking a coinflip weighted in your favour.
To this day, I think that's why most people who hate Deo-A, hate Deo-A; it's not broken competitively per se, but it imposes coinflip matchups that prevent certain builds from thriving.
On another note, I forget when Matame's Froot RMT and Kamikaze's Sun Psyspam team with Milotic were created, but those teams deserve a s/o too as some of the first Psyspam builds.
Eventually, during np: DOU Stage 1, Trick Room became more popular, people were coming up with sets like bulky seismic Kangaskhan, Zapdos/Fini cores, CurseLax, etc. etc. and eventually we reached the point where bulky offense became the new meta. Psyspam was still potent and annoying to face up against, but setup-oriented builds were a lot safer and more consistent to use. I had moved on at that point.
Stratos / Kamikaze / Blood Totem brought back Psyspam rain in April, and the archetype gained more mainstream recognition because more high-level players were using it. The important development here was that Deo-A was using Choice Specs, not Focus Sash, and was doing like 80% to Ferrothorn inside of Psychic Terrain which was insane. People began realizing that Psychic Terrain let Deoxys-A get away with riskier, more offensive sets.
However, non-Sash Deoxys-A is only good until people start expecting you to not be running sash. It's a set that plays on people's conventional expectations of needing to play around a Sash, so you can bust out a wild set and score an OHKO that your opponent didn't expect to be possible. Once you knew [insert username here] liked using Specs Deo, you were able to play around it and sometimes even exploit it, and I feel most people that were using specs eventually stopped using specs.
Yes, high level users like qsns players still whip out items like Specs, Z moves and Life Orb in important matches like Snake, lategame seasonals, etc. but again, these sets mainly work by challenging people's expectations of a mon. It's also worth noting that B01 team tours like Snake, SPL etc. are much more encouraging of obscure and innovative sets that only need to catch people off guard for one important match, and even B03 tours can foster this type of building when it's two experienced users facing each other. It's no different than Chase's infamous Linoone team, etc. etc. but the thing is a good tournament team isn't necessarily the same as a good all-purpose team where you want consistent results over time.
Arguably, Sash is still the most consistent item for the long haul, but from time to time people will pull out other items because they know they can.
^ This guy tho
Was Deoxys-A's dream come true.
Deo rain now had an actually good fighting-type to break Ferro, and Marshadow's role as a fast attacker with perfect coverage was the perfect addition to almost every Deo-A hyper offensive team that already existed. Furthermore, Marshadow dropped the viability of both Trick Room teams and many of the bulkier setup balance builds that Deo-A hated. We're talking about Deo-A again because Marshadow made it good again.
And to be fair, we were so sick of the setup meta at this point that a lot of us welcomed Marshadow with open arms, even though we knew it was potentially dangerous for the meta. And I mean, I was one of those people even though I didn't vote in np: DOU Stage 3 - the setup-heavy meta got pretty trash after a while and I think I still enjoy the current meta more. But Deo-A isn't broken because Deo is Deo. Deo is broken because we created an environment that has limited strategic options for gaining the upper hand over the opponent, so now we're turning to: Deo-A, Stealth Rocks, and setup sweepers like Mega Scizor that are more resilient to Marshadow.
Fwiw though I laddered a bit with Rain Psyspam during DLT and found it to be one of the least consistent builds, followed by Sun Psyspam. People generally know what it does and know how to play it, imo. Sand, stealth rocks, and hail really are a pain for it too. But yes it is annoying to fight and very effective against the right matchup.
But tbh, I really don't care if Deo-A gets banned or not, because...
Deo-N can just fill the void. I'm not going to lie, the 30 bst drop to both Psycho Boost and Superpower matters more than I initially thought. The Atk drop is especially bad when you're trying to hurt bulky steels like Ferrothorn. But, under Psychic Terrain Deo-N almost as potent as Deo-A as far as I can tell based on initial tests. There's also Deoxys-S which, while a much weaker mon, is a mon that actually outspeeds Scarf Jolly Lando, has the bulk to pull off an offensive item like Life Orb, still hits like a truck under Psychic Terrain thanks to an OP Psychic STAB, and has the bulk to set Stealth Rocks -- akin to the SR deo-a set Miltankmilk likes to bring :)
There is probably a subset of people that think that the power nerf to Deo-A is enough to balance things out. If that's your view and that's all you want - that's great! Most mons we suspect don't give us the option to just slightly nerf it, but we can do that here.
However, if you hate Deo-A because of the coinflip matchups it imposes, please realize that Deo-A is not the reason Psyspam archetypes are thriving right now - that's on Marshadow breaking down the fat setup teams and breathing new life into offense.
One interesting idea I've heard a few people toss around is that we keep Deo-A, keep Marshadow, but also free Jirachi into this meta. Jirachi was one of the best Deo-A checks before, it can probably run some sort of Kasib Berry set in response to Marshadow, and breath a bit of fresh life into setup and Trick Room without OP'ing it like it was before.
I'd want to play this hypothetical meta for a few weeks first to test it before buying into it, but I think it's a really interesting idea.