The process the question describes is both possible and may still be underpowered
The description of the supernatural ability steal spell-like ability, in part, says
At 5th level and higher, [i]f the target is willing, a spellthief can steal a spell-like ability with a touch as a standard action. This spell-like ability… can be of
any level up to a maximum of one-third the spellthief’s class level. A spellthief can select a specific spell-like ability to steal; otherwise, the DM chooses the ability at random. If the ability has a limited number of uses per day, the target must have at least one such use left, or the spellthief can’t steal the ability. If the target can’t use its ability at the present time (such as a summoned demon’s summon ability), the spellthief can’t steal it. A spellthief can use a stolen spell-like ability once. For all purposes (caster level, save DC, and so on), treat the spell-like ability as if it were being used by the original possessor of the ability. A spellthief must use the stolen spell-like ability within 1 minute of acquiring it, or it is lost harmlessly.… (Complete Adventurer 19 and emphasis mine)
This reader has always viewed A spellthief can use a stolen spell-like ability once as making a specific exception to For all purposes (caster level, save DC, and so on), treat the spell-like ability as if it were being used by the original possessor of the ability. However, I can imagine a DM worried about a spellthief wanting to read it another way.
That's because—as this reader parses the ability—, out of combat, a spellthief can use the limited-use spell-like abilities of any allies and unconscious or restrained foes any number of times as long as the creature has at least one use of that spell-like ability remaining. This can be an issue.
For example, a spellthief may not be able to befriend a rejkar (Monster Manual III 140), but knocking unconscious a rejkar and grabbing its fabricate spell-like ability so that the spellthief can use at will that fabricate ability instead of that evil demon-goat? That's a pretty significant score.
Similarly, a spellthief is often encouraged to obtain a familiar, and the imp (Monster Manual 56) has as a spell-like ability commune 1/week—giving the spellthief, essentially, an at-will, no-XP-cost commune effect, and that is a game-changer.
And did another PC take 10 levels of the prestige class master of the secret sound (Dragon #297 78–9)? Borrowing that PC's spell-like ability the secret sound so that the spellthief can replicate any 0- through 6th-level spell as a spell-like ability is pretty much the ultimate score.
However, the primary balancing factor is that, with rare exceptions, a spellthief can't multiclass and also advance the ability steal spell-like ability. Thus the typical spellthief must be at least a level 12 spellthief to steal a 4th-level spell-like ability, a level 15 one to steal a 5th-, and a level 18 one to steal a 6th-, and the typical spellthief won't ever be able to steal anything higher. Many campaigns never reach such levels. (And I can imagine actually playing a spellthief through those early levels being quite the slog!)
Of secondary importance is that the ability steal spell-like ability—like, for example, the special ability favored enemy of the ranger—is campaign-dependent. It relies on other creatures in the campaign possessing spell-like abilities to steal! If the party cleric or wizard is comfortable calling creatures, knocking them unconscious, and storing them so the spellthief can swipe their spell-like abilities, that's useful, but then the spellthief is beholden to the party cleric or wizard or whatever, and there's no easy way—short of scrolls and Use Magic Device skill checks—for the spellthief to do that himself. Even the two feats that the spellthief devotes to getting an imp familiar are 2 of his only 7–10 feats that the typical spellthief will ever get, the spellthief not having from its class any bonus feats.
Finally, keep in mind that the spellthief must use the stolen spell-like ability within 1 min. of the theft. He typically won't be starting an encounter with a massive suite of spell-like abilities unless standing orders see him taking 10–15 seconds of every minute to touch party members or his familiar… and that's a little weird and will probably annoy party members if not also the familiar.
Nonetheless, I understand your concern. In a high-level campaign wherein the PCs already possess significant spell-like abilities, a spellthief can be—outside of combat—an extremely useful problem solver, especially if the spellthief's in cahoots with the party's other casters and spell-like ability users. In combat, though, because the spellthief must take a standard action to touch a creature to employ the ability steal spell-like ability then usually take another standard action to activate that stolen spell-like ability, he'll have to rely on other tactics… and the typical spellthief just doesn't have many: his sneak attack is half that of the rogue, his caster level is both typically half his level and Charisma-based (mandating he possess several high ability scores for maximum efficacy), and if he spends his feats on making himself self-reliant he's not spending those feats on fightin' monsters (unless his self-reliance helps him fight monsters, of course).
To be clear—and to demonstrate how unattractive these downsides are—, this DM (a fairly competent optimizer) has never used an NPC spellthief as a foe in his campaigns, and this DM's players (several possessing optimization skills on par if not better than this DM) have never played in his campaigns a PC spellthief. This player has played a multiclass spellthief in a short E6 campaign—finding the spellthief a more interesting source of sneak attack than the traditional rogue—, but in seven sessions of play never stole even a single spell. (To be fair, the PCs were, most of the time, fighting the police in Las Vegas. The Vegas PD apparently doesn't have casters on staff.)
So while it's possible—in the right campaign—to see a spellthief dominate the action and solve all the problems, it's not very likely. Clerics, wizards, psions, artificers, and even some rogues and martial adepts will usually be better-suited to problem-solving in most campaigns. In the correct campaign, though, the DM may find himself with a PC who's a level 15 spellthief who has an imp familiar and who spams commune to solve his—and the everyone else's!—problems. If that occurs—and you find such a PC unbalanced (knowing the answer and doing something about it are two different things, after all)—, then it's time to talk over with the player his choices and, perhaps, reexamine the spellthief.
