No, because once the contracts with VC2 are signed etc. they can't change the terms, so VC3 can't swoop in anymore in the same round.
And even if VC3 swoops in during negotiations with VC2, it requires the founders to be pursuing that (and VC1 would be aware). Whereas with the ROFR the founders have no choice.
Finally, VCs suffer from herd behavior. So it is very plausible that many VCs arrive at the same valuation - the valuation of the VC leading the round / the valuation of the best-reputation VCs. If foo VC values a company at $10M, but Sequoia comes in at $20M, 99% of the time foo VC will second-guess their valuation and match Sequoia.
The founders have a fiduciary duty to all existing shareholders (angels, early employees, etc.) to exactly be pursuing VC3 at the same time as VC2, before anything is signed, and to take the best deal. They already have no choice.
Your point about herd behavior is well taken, though. And the result is that the VCs moan and groan, but ultimately the price goes up, and the entrepreneur wins, because they get the best valuation possible. (I've been in the room as an angel investor, and I was sure happy when the valuation went up 25% when a second VC got interested in the B round.)
The only counter-argument I can see is, in your example, if Sequoia's money really is greener than fooVC's (which there are long-standing arguments for and against).
No they don't have a fiduciary duty to negotiate with everyone. Founders routinely arbitrarily decide certain VCs are not the right fit (basically, they don't like them).
And even if VC3 swoops in during negotiations with VC2, it requires the founders to be pursuing that (and VC1 would be aware). Whereas with the ROFR the founders have no choice.
Finally, VCs suffer from herd behavior. So it is very plausible that many VCs arrive at the same valuation - the valuation of the VC leading the round / the valuation of the best-reputation VCs. If foo VC values a company at $10M, but Sequoia comes in at $20M, 99% of the time foo VC will second-guess their valuation and match Sequoia.