Lingering song is needed depending upon DM's interpretation. Some rule that you can only have one of the "Inspire" abilities actively maintain at one time. The rules actually allow for you to start one and maintain it even while starting another, but not everyone sees it that way.
Interesting. I would have thought that the existence of the Combine Songs class feature some Bard PrC's get in CWarrior and CAdventurer would make it pretty clear Bards are at least not intended to maintain multiple songs at once as the norm. And since when was it required to use multiple songs per encounter in order to win?
Five rounds is not quite enough for combat (experience talking here).
And in my experience, SIX rounds (the round you started counts, too) is almost always enough.
When you go into "alpha strike" mode and get ready to strike with full buffs up and running, you need more than five rounds.
Is this normal? In all of my games, the occurances of us buffing up like crazy and charging in like a SWAT team are rare, and the DM would not normally present too many situations to make use of that "tactic." Maybe for scry-buff-teleport, but I've also never actually seen that. Also, I have to wonder, you say Lingering Song is not needed only by a specific DM ruling, but your example of why it's useful is just as much DM fiat. Like I said, in my games, those SWAT scenarios seldom exist, so unless the DM allows that, Lingering Song is of no value for that purpose.
If, and only if, your DM goes with the rules as written (where you can maintain multiple Inspire abilities), then Lingering Song is not needed.
I think it's a great feat, just not for most bards. Most of the other feats on the OP's list solve problems Lingering Song was meant to make less devastating. For example, Melodic Casting came out after Lingering Song. before it, your best bet was to start a song, let it linger for the extended time,and start casting. With MC, you no longer need to stop performing. Similarly, you could use lingering song to half-arse "covert singing" such as "rob, rob, rob the merchant!" basically doing the performance away from suspicious ears and riding the effect long enough to walk in and do whatever. With Subsonics feat, that's also not an issue at all any longer.
In conclusion, I think Lingering Song's a great feat to ~30% cover the functions of each of a number of other feats, and thus a good choice for a feat-strapped Bard. But if you can afford Melodic Casting, Subsonics, and maybe even Somatic Weaponry, it becomes far less important.