We can't say for sure DmC was what killed the franchise, DMc "necrosis" started before that. Let me explain:
There was a very prosperous DMC community forum in the internet ( most of you probably know) called Devil's Lair. That community was at it's best when after DMC3 fans was excited with the idea DMC4 could be so great as DMC3 was.Voice actors like Reuben, John and Dan were members too and usually went there to exchange opinions with the other fans.But...
After DMC4 a lot of fans just abandoned the series, maybe because DMC4 had failed their expectations, others were furious about how the characters were portrait and so on. Cat, the forum's owner, just let the forum gently die ( she expressed her disappointment towards what they have done to Vergil and other characters).
Bayonetta came and people started to proclaim Dante was dead and he was trash since Bayo would take his place.
Capcom so decided to refresh the franchise doing a reboot( what could be a good idea or not) to revive the interest on Dante as a protagonist.
Was the reboot the only way? Maybe not, but sure a lot of people had ask Capcom before to change things about DMC, but Capcom never did, since they feared fan backlash, so classic DMC was left in Limbo.
Now you can freely conclude whatever you want.
''That community was at it's best when after DMC3 fans was excited with the idea DMC4 could be so great as DMC3 was. Voice actors like Reuben, John and Dan were members too and usually went there to exchange opinions with the other fans.''
I'm sure a lot of fans were disappointed with DMC4 in several ways... but isn't that the case after each DMC? DMC1 created expectations, DMC2 didn't fulfill them. For the people who liked DMC2, it created expectations for DMC3, which weren't met either. If people hadn't played DMC2, they expected DMC3 to return to DMC1's style. Once again, expectations weren't met. So I doubt a huge deal of fans of the entire DMC series just decided to abandon the series after DMC4. Whatever people may say, DMC4 was not some kind of disaster - most people were pretty positive about it, and it got positive reviews. And DMC has always been pretty vague, and some people stuck with the series even after DMC2, which is still considered a bit worse than DMC4.
The quote in orange tells me that that forum was filled with people who liked DMC3 most - they weren't fans of the entire series per se, but mainly DMC3. That would explain why so many fans seemed to abandon the franchise after DMC4 (if they did): because they were fans of DMC3 and DMC4 wasn't too similar to it. It's not surprising that when DMC4 turned out to have a lot of backtracking and a slightly different Dante (again), along with a replacement for Dante, and no Vergil, that DMC3 fans were disappointed. Some people even expected DMC3 to be the first game in a sensible story, as it was a retcon... so not going through with Dante (and possibly Vergil) but instead going with Nero wasn't a popular choice.
It seems to me that the DMC fanbase is fluid: each DMC game was pretty different from the last, which means that each DMC garnered fans, and also alienated fans that liked the previous installment. That said, the gameplay is still the most important aspect of DMC, and it's been really nice since DMC3. DMC4 did make some people angry, but I don't think anybody has studied how many fans ''abandoned the series'' -- that phrase is usually used as a threat.
The reason for the reboot is debatable -- I think they might've done it because they didn't know what to do with Nero. Explanation of who he was only came a long time after DMC4 was finished, so maybe they didn't have any ideas until Bingo came up with the idea that he's Vergil's son.
Going off what I wrote in the first few paragraphs, it's possible Capcom wanted Devil May Cry to have a fanbase that sticks with the series for the story too, not just the gameplay. DMC4 got a lukewarm response from their latest fans (the fans of DMC3), but it still sold very well... so I think Capcom realized there was a lot of potential for making money in DMC. Basically, Capcom was greedy - but they didn't realize people liked DMC for more than just ''gameplay + story''. Changing the characters and the style and atmosphere of Devil May Cry so drastically... it changed the entire personality of the series, and that's just one reason why DmC failed.
Having said all of this, it's still a very tough subject, and nobody here worked for Capcom on DMC, so I suppose we have no idea what Capcom's thinking. It's annoying just thinking about this mess of opinions and the franchise, because I don't have all the answers either.