Perhaps groaning is a bit much, but then again, it depends very heavily on the circumstances. If the team's managed to show the fans that they can pull off flicks around the corner with ease, if they're playing free-flowing football (our trademark, after all) then the fans won't be so concerned to see them try it. But when we're trailing, and given the football we've played this season, it's not unnatural of the fans to expect the team to put more effort into the simple things: getting into advanced positions, making forward runs, playing at a higher tempo, working the ball into the box, etcetera, as opposed to trying flicks around the corner that then go out and give the opposition time to retreat into their ten-man shell again.
Secondly, it's not about supporting particular players, it's about cheering on the team. I agree with you: Beyond Sandro, Townsend (academy man), Dawson (plans to retire here) and Freund, I can't find a genuine emotional connection with anyone at the club, AVB included. But the point behind cheering is this: you show love to the team, the eleven players on the field, you roar them on and you try to help them win. This is something the players themselves want you to do, and often will ask you to do in order to help them win. However, they will often not win even when you cheer them on. And unlike in the old days, when that didn't matter so much given that players would likely stay at one club for years, allowing them to effectively 'make it up' to the supporters by performing better the next time the fixture rolled around, in the modern era, one win often means everything in terms of players staying and the club progressing. And the fans all know this: they know that there is a risk that despite their cheering, the team will fail to meet their objectives. And they know that when the team (who are, after all, eleven individuals) fails to meet its objectives, the players tend to agitate for moves away, despite the support shown to them both as individuals and as a team by the fans. So firstly, there is no connection between the players and the fans, and secondly, cheering the team on and then watching them narrowly (This is important) fail is painful in the extreme given the heights we're aiming for and the danger not hitting those heights poses to us as a club (namely, losing all our best players and regressing). This generates a sense of cautiousness among the fans: they are intensely reluctant to attach themselves to this group of players, this team, lest they be burned when they fail (as is looking somewhat likely at the moment). The team first needs to show the fans it can succeed before the fans respond by urging it to succeed. It's not pretty, but this is unfortunately the face of modern football. And, after being burned so many times, I don't blame any Spurs supporters that wait for the team to show them something special before throwing themselves in completely again, at least while we're still up there challenging.
You know, it was so much simpler in the Jol era. We were just emerging from a long period of being ****e, but after having been ****e for so long, even a little progress was something to be grateful about, and we weren't as on edge then because there wasn't as much at stake: worst comes to worst, we'd slip back into mid-table mediocrity, and considering that we weren't far away from it anyway, that wasn't as threatening a prospect as it appears now. We could sing freely, safe in the knowledge that this team failing wouldn't affect us much, while this team succeeding would give us no little amount of joy. That's why our support was good during the Jol days: because we were ****e, not in spite of it.
Now, we've risen so far that we have a long, long way to fall, which generates nervousness. But even success isn't as satisfying, because it merely staves off the danger of our team being decimated for another year. If we get top four this season, I'll be more relieved that overjoyed, I suspect, something I never thought I'd be saying five or six years ago. Because even one year out of the top four is a cue for the likes of Lloris and Verts to push for moves away, meaning we need to keep it up continuously if we want to get anywhere, meaning one season of top four doesn't have the impact now that it did in 09/10 in terms of instilling belief in the fans. So that generates an impatience and nervousness in and of itself.
Sigh. Modern football really is eating itself. Hopefully we'll win a trophy this season: that would send me (and, I suspect, a lot of us) into dreamland, because that is something permanent: players may come and go, but that will be etched into our history forever, and so its significance will remain undimmed. For now (until that new stadium comes up, anyway), in terms of geeing up the fans, that's probably the best we can hope for.