Some may be getting a bit too hung-up on direct continuation of precise content of the previous, methinks.
Did Fallout 2 have an ending, yes, any one of four endings (as I seem to remember).
So, which ending should Fallout 3 have continued?
And precisely how does one continue something that has ended ... it's a contradiction. There was indeed an ending in Fallout 2 (even though you could continue playing, doing nothing really).
The developer chooses the what ending is to be considered as canon if there are multiple iterations of to choose from, and makes the continuation according to that. There's nothing more to it. The continuation from from Fallout to Fallout 2 was not straightforward "begin where the first ended" - and Fallout had an ending too, yet it the story was continued.
Those endings are not definite storywise, though. The world doesn't cease to exist after the protagonist does his deeds. It's just an event in the region. So there are plenty of possibilities to go with, with filling the blanks in between. Like how Shady Sands turned into NCR, how Arroyo was born, how the Chosen One was the Vault Dwellers grandson. The world continued. There was a straight relation between the stories. And as I said, I don't think the number matter. Fallout 3 could've well been named Fallout: Capital Wasteland, and the effect would've been the same as it is now - and that would've even made a bit more sense as Fo3 was not a continuation of the story of Fallout 2. But this is not really an argument, they call their games as they please - that does not affect the content. At the time when Fo3 was announced, the number did evoke certain expectations, but not so much anymore, though.
Sequel continuation. The scenarios and content type of plays though can indeed be continued with all of the essences that the previous Fallouts had, and that is what Fallout 3 did so masterfully, at the same time updated the dated mechanics, dropping the board-game combat, and making the game more fully RPG.
Yes, there will be complaints from those that prefer a mix of role-play and board game play of the early Fallouts, but fallout 3 has evolved into a fully blown Role Playing Game (RPG). Yes, in the Fallout apocalyptic scenarios there is naturally a lot of combat play along with the role play, as it was in the early Fallouts, about half and half at least, and it was easy to seek out more combat situations if you wanted to in those early Fallouts, and similarly in Fallout 3 it is just as easy to do more combat in preference to role-play interactions. Remember though that if you have chosen to do more combat in preference to role-play then it would be wrong to think that it is all about combat when there is an abundance of role-play in Fallout 3 that you could have done, more that there was in the early Fallouts in fact, partly because of the increased amount of content Fallout 3 has but the role-play situations were also vastly increased in size, and no doubt they will be in the next Fallout sequel which will be Fallout 4, and of course it should be 4 not 5. Fallout 3 had all the essences of the early Fallouts, that cannot be denied, apart from the board-game play.
Bethesda has a reputation of improving a previous version, that's what they did to the early Fallouts when the made Fallout 3, and will no doubt do again in the next Fallout, which naturally will be called Fallout 4, simple.
Needless to say I disagree with the "improvements" over the originals on most regards, and with the "full blown RPG" -stuff (where does that come from?). We've been over it more than once, so you know my point of view about it -- Beth didn't
improve upon, they turned the core of the games inside out and made an apple an orange instead of refining the apple to a better apple, and could've done even that more carefully and faithfully to the predecessors both, gameplaywise, structurally an writingwise, and so on -- an apple-orange juice or a pie, if continuing the food anologies. Fallout 3 had all the potential of the originals, and even more with the technology of today, it's just a shame they didn't use it to refine Fallout, but to refine some of their earlier expertise. Who knows what would've been the result had Beth made a fresh approach to making their games, instead of going on with the concept they have been doing since day one. I do agree with you on one thing, though... The way from Fallout 3 is up, so now's the time for Beth to start improving the franchise.
And, as I've said, I don't really care what they call their next Fallout.