Yes, sometimes they do.
No tech co put this in their standard T&Cs, of course, but in a “send it to legal for redlines” situation the attorneys on the customer side will often add this.
Their argument is they are invested in you, and want an out if you sell to a vendor they don’t want to work with.
You can say No, and usually, they will give.
If they won’t, a decent compromise is they can terminate — but get no refund for the remainder of the term. Yes, this sounds silly, but often it may be enough to satisfy Legal.
In the end, it’s possible you’ll have to agree to this a few times. And if you do, and are acquired — the acquirer may make you go and get agreements from larger customers to remain customers before the deal closes. But usually. They will roll with it …