There are two advantages to Rapid Summoning that I can see - the conjurer can put an ally in place sooner, and she can avoid the problem of having to make a Concentration check if injured while casting.
At 1st level, a wizard with single digit hit points who is hit is more likely to fail to cast a summoning spell because she's been knocked unconscious than because she failed a Concentration check, while at high levels the Concentration check becomes almost a formality. If she's taking enough damage in a round that it isn't a formality, then she has bigger problems to worry about. I don't think Rapid Summoning provides more than a nominal advantage here.
Being able to put another body on the battle map immediately on her initiative count can be nice. It can block an enemy's charge line or provide cover, for instance. There are other ways to do that sort of thing, though. Not such a big deal, in my opinion.
A rapid-summoned monster can't make a full attack in its first round. It can use a single standard action, but then has to endure whatever the enemy throws at it. Summoned monsters at low levels will generally be killed by a single hit, and at high levels they're little more than speed bumps in combat, good for blocking off lines of movement but not much else.
The variant provides an unambiguous advantage at lower levels. Of the SM I creatures, only the badger and scorpion lose out on full attacks. At SM II, it's the lemure, scorpion and squid (how often does that one come up?). But at SM III and above, many of the monsters can make multiple attacks as a full round action. They probably won't survive more than a round or two, so the balancing factor with respect to getting them in place sooner is losing out on one or more first round attack rolls, which might be 1/3 of their total.
A lot of the fun of playing a conjurer is in summoning just the right creature for your party's needs. Out of combat, the summoning time is irrelevant. In combat, it can make a big difference. Three times in just one LEW game, I've seen summoners (they were druids, but the point is unaltered) declare their intention to summon a monster only to have the situation change or even the combat end before the spell could be completed. How boring!
The variant makes conjurers "better" - not necessarily particularly more powerful, but certainly more fun to play, since they have so much more chance of using their signature tactic.
Would I choose Rapid Summoning over a raven familiar holding a wand and croaking command words, the +16 Spot check of a hawk, the blindsense of a bat, or even the +2 Fort save from a rat familiar? Maybe, maybe not.
I vote YES.
I'd probably vote yes to all the other wizard variants on that page, with the exception of the Enchanter cohort one.
