I would not suggest that it is "always" advisable to order and perform a termite inspection particularly if there is no evidence of infestation.
However; if termite damage is suspect, then it's in your client's best interests to have an inspection performed. If the bank must see it, then so be it as it may resolve the issue in getting the necessary repairs completed in order to close.
Just another hurdle....
Prudential Connecticut Realty
The biggest reason not to make a termite inspection a contingency in the contract in this case is this though: If the seller can't or won't clear it, and the bank knows about it, you're stuck. Can you authorize and pay for termite repairs on a property you don't own yet? Yes - if the seller allows it - but what if something goes wrong and you don't close? You're still stuck with the bill, and likely, the seller will use part of your earnest money deposit to pay it. Do the inspection - but keep it off the contract - that's my vote.
Speaking as a lender, as long as you do not write a purchase contract addendum asking for seller credits for termite work, the lender does not need to know, nor do they care to see the Termite Inspection report. As for a 3% closing cost credit if you want to find a creative way to get your buyers credit. Of course, if there is visible termite damage, it might be noted in the appraisal, but that is an entirely different issue.
Order all the inspections the buyer is willing to pay for. This is a big investment...your buyers should know exactly what they are getting.