I really don't enjoy it when people limit the amount of times a game in a series can list. First off some games in the series are very different from each other. The Final Fantasy series is the premiere example of this. Final Fantasy VI, VII, IX, and X are all listed and are all very different games despite being from the same franchise. This also can hurt some franchises as some entries will appeal to different players. For example Skyrim will likely beat Morrowind in the list thus in your hypothetical list Morrowind wouldn't chart. However I feel that most people would agree that Morrowind deserves a spot on the list if it garners the votes because it appeals to a different set of gamers than Skyrim does despite it being of the same franchise and basic formula.
This is a serious problem with limiting voters to one game per series, as several people acknowledged earlier. I don't know that I've heard a great solution to the problem. The option where only one game per franchise can make it would eliminate Persona 2/Morrowind/FF12 even though some people who like those games want nothing to do with Persona 4/Skyrim/FF6. It's entirely possible that results in what most people would consider a worse list. Of course, it might also make a list that's simply interesting in a different way.
I think someone suggested having everyone vote normally and then only giving each series one "slot" in the overall list (determined by its top vote-getter?), with a note underneath showing the vote totals for other games in the series. That's more of a cosmetic change from the current format than anything else, but maybe it's preferable to people who want to see a more diverse top twenty-five.
I also don't like the idea because while it may seem better off when reading say the top 20, but as you go on you will start to get a lot of games that have no business being on the list , especially when you get down to the bottom 20. There is a reason why scrolling through the list you will see a lot of repeats of the same franchise, because they are franchises made by quality developers. Atlus for example is a fantastic developer. However if I were to limit the Megaten series to one entry than only one of their games would appear (two if you were to count Persona as separate from Megaten). Outside of Megaten,, what has Atlus made that could possibly chart? Etrian Odyssey is the only other series they really have. The same can be said about Square-Enix, Bioware, Falcom, etc. I think that the only RPG developer that regularly works on different IPs with their games is Obsidian, which two of them were sequels to already popular RPGs. By limiting franchises to one entry you are essentially limiting the entires of each developer. Limit Square-Enix, Atlus, Bioware, Nintendo, Bethesda, and Sega to only a few games at a time, and the list will start looking a lot less "essential" after the first thirty games or so.
On a list where a given series could only appear once, I think you would see Atlus place for Persona, SMT, Etrian Odyssey, and as the publisher of Tactics Ogre. Square-Enix would place for Final Fantasy, The World Ends With You, Chrono Trigger, Dragon Quest, and more. Bioware has Baldur's Gate, KOTOR, Mass Effect, and Dragon Age. And Nintendo has Mother, Fire Emblem, Paper Mario, Xenoblade, and (more or less) Pokemon. Sure, these companies would get
more entries if they could score multiple games within each series, but their prominence as developers would still be pretty obvious.
EDIT: Understand that I'm just thinking through this myself. I don't have strong feelings about changing the rules or trying to diversify the top twenty-five.