Probably not, no private company has the ability to tell all its suppliers "thou shalt not do business with <some other company>". They lack the pull to compel them to do so. The closest would be things like what MS did back in the 90s, and got them in hot water with the anti-trust case against them.
Do you seriously think that you can go to all your vendors (if you were a business owner) and tell them, "You can't use Atlassian when working on anything you sell us." How will your business actually compel all those vendors to drop their use of Atlassian for that work? How will you verify compliance and why should any of them sign a contract with you with these restriction? And if they do, how will you avoid anti-trust violations because almost certainly the only way you could talk them into signing such a contract would be to be a massive company throwing your weight around (like MS did with hardware OEMs back in the 90s, among other things).