I don’t have canon evidence to back this up, but I think it probably comes down to a matter of legality and ethics.
We know that you can’t use Veritaserum on students. We know that the use of Veritaserum on students is regulated (thanks ike and Mac in the comments for correcting me). In a similar way, I’d expect Legilimency to be restricted, perhaps even banned.
Using it on a student is a clear violation of privacy, and abuses the relationship between teacher and student. If Snape was using Legilimency on students on a regular basis, somebody would eventually realise that he was doing it, and he’d probably get kicked out. You can think of plenty of situations where it might be useful (did the dog really eat little Johnny’s homework?), but not where it would be necessary.
In Muggle laws, we have innocent until proven guilty. This restricts police powers to search people (note IANAL). For example, UK police generally aren’t allowed to search somebody unless they have reasonable suspicion that a crime has been committed. I think this rule probably applies to Legilimency and Veritaserum.
If we look at the specific instance in HBP:
“I didn’t mean it to happen,” said Harry at once. His voice echoed in the cold, watery space. “I didn’t know what that spell did.”
But Snape ignored this. “Apparently I underestimated you, Potter,” he said quietly. “Who would have thought you knew such Dark Magic? Who taught you that spell?”
“I — read about it somewhere.” “Where?”
“It was — a library book,” Harry invented wildly. “I can’t remember what it was call —”
“Liar,” said Snape. Harry’s throat went dry. He knew what Snape was going to do and he had never been able to prevent it. …
The bathroom seemed to shimmer before his eyes; he struggled to block out all thought, but try as he might, the Half-Blood Prince's copy of Advanced Potion-Making swam hazily to the forefront of his mind.
And then he was staring at Snape again, in the midst of this wrecked, soaked bathroom. He stared into Snape's black eyes, hoping against hope that Snape had not seen what he feared, but –
Umbridge aside,1 this is the only instance I can recall where Legilimency or Veritaserum were used on a student outside Harry’s classes. Here, Harry has already admitted that he used Dark Magic, and Snape walked in on him red-handed: the guilt is clear.
This is more than just a schoolboy prank: these are very dangerous (probably life-threatening) injuries. If it wasn’t Harry, this would probably be grounds for expulsion or prosecution.
As serious as stealing from a teacher is, it isn’t really on the same scale. To me, Snape telling Harry he “knows” who stole his ingredients looks more like an intimidation tactic than anything else.
1We know she planned to use the Cruciatus curse as a disciplinary measure, which is definitely illegal. She was also overenthusiastic with the Veritaserum, and used it in large quantities. I don’t think what she did was really legal.