In my opinion, no, not at all. Like you said those 3 states are most likely our top 3 "zoo states", I think Texas can easily give Ohio a run for its money and perhaps California and Florida as well.
Let's start with Texas! DWA is a fantastic facility and while its habitats are not always top-notch, it easily makes up for this with tons and tons of rarities. Then we have Fort Worth and Dallas, both also some real nice facilities. Fort Worth has a great collection with some rarities, and many of its habitats are quite well done especially MOLA. Dallas excels in housing and breeding hoofstock species and while the monorail has closed, I've heard through the grapevine that there are plans to get those habitats back on view. Not to mention, the fantastic Giants of the Savanna habitat which showcases one of the nation's only elephant mixed-species habitats with the world's tallest and heaviest land mammals being mixed with one another among various other species. There's also Gladys Porter which also has various hoofstock rarities like gaur and harnessed bushbuck. Another ungulate-focused facility is Fossil Rim with numerous ungulate species living in open field habitats much like SDZSP or The Wilds. Many of their hoofstock species aren't held by several other facilities and they have done a great job breeding and sustaining these populations along with a few others. They also have one of the best cheetah breeding programs in the nation with nearly 200 cubs born. Dallas, Gladys Porter, and Fossil Rim are all certainly must-see zoos for ungulate nerds like myself. We can't forget about Houston and San Antonio as well, both facilities have slowly been improving over the last few years and it looks like things will continue to get better. Houston just opened their Pantanal habitat in 2020 and plan on opening their new Galapagos habitat early next year. Both of these have/will significantly improve Houston's record in the zoo world. Being an elephant nerd, I can't fail to mention that Houston currently also has probably the best Asian elephant breeding program in the US (besides Ringling) with 5 calves under 5! Moving on to San Antonio, they just released new plans a while ago that show they plan on expanding significantly and adding several species. They also just announced that they will be welcoming gorillas back to the zoo in the next few years as they begin constructing a new gorilla habitat. San Antonio has some big plans for its future and I'm certain this will elevate its current status in the zoo world. Then there are numerous smaller, less-known zoos that are pretty good facilities as well including Ellen Trout, Caldwell, Cameron Park, El Paso, and Abilene. Obviously, there's also SWSA but that's technically an aquarium/theme park so I'm not sure it belongs here.
As for California, there's SDZ and SDZSP. Don't even need to explain those two, obviously some very strong contenders due to their very strong collections and several amazing habitats. Two other CA gems that don't get the spotlight that much are The Living Desert and Los Angeles. The Living Desert is a fantastic facility with top-notch habitats and from photos I've seen, some of these habitats come close or perhaps even beat out SDZSP's field habitats. Now the park's habitats are without a doubt, bigger and more species-rich but there are several spots in the Living Desert's habitats that just blend in very smoothly with the surrounding desert/plains which make them look very naturalistic. The same cannot be said about SDZSP's rather arid habitats with fence lines and bomas often popping up all over the place. Not to mention, the Living Desert's several rarities like short-beaked echidna and yellow-footed rock wallaby. As for LA, it is a fantastic facility with numerous rarities like Calamian Deer and bald uakari that really make it stand out. While many of the habitats are sort of outdated, the zoo has slowly been working on fixing up various sections of the zoo which has resulted in a slow but steady transformation. Then we have Fresno Chaffee Zoo which is another fantastic facility that has slowly been improving its various sections, the current zoo is completely different from the zoo it was just a few decades ago. We also have some facilities like Turtle Bay Exploration Park and Micke Grove Zoo that have numerous bird rarities but get little to no attention on here. I'm going to stop myself here since this post has already gotten humongous but we can't forget about the various other zoos in the state that are pretty good but not amazing like San Francisco, Santa Barbara, Oakland, and Sacramento plus major aquariums like SWSD and Monterey but again, that may be off-topic here.
Florida also has tons and tons of pretty great facilities but I can't really think of too many facilities that really stand out besides maybe DAK and Miami. I won't get into that because, like I said earlier, this post is long enough. Sorry about that!
But yeah, besides these 3 states, I think you're correct that Ohio is probably one of the best if not the best zoo state. Also, this thread may be of interest to you:
Best State for Zoos
