It's not just a feeling either; in some cases this is a proven fact. CC2 had to tone down the ultimates and remove wall fighting from the Ultimate Nina Storm series between 1 and 2 to make the game work online. And then between 2 and Generations the story mode was given the axe to make way for big gameplay changes to better fit the competitive (read: online) experience.
Then we get some very suspicious vibes leaning towards this from Namco with the Soul series at the very least (not sure about Tekken since I've never bothered to play it bar one time at an arcade), with Soulcalibur 4 marking a significant loss in single-player content compared to 3 and to a lesser extent 2, along with it being the first game in the series to feature online. This trend is even worse in 5, where only one quarter of the intended story mode ended up in the final cut of the game, characters don't have individual endings in arcade mode, and there is no "play till you lose" survival mode that's been present for every game in the series until this installment... and almost half the achievements are ones that can only be done online. There's nothing concrete, but it seems like online versus was a big priority, to the detriment of single-player content.