Unless something has changed in the most recent CBA they do. Trade kickers and player options are really the only pain points teams can apply to a max contract since the payment structure for a max contract is set in stone.
It appears I was wrong. After reading the rule above? Otto Porter was allowed to have a trade kicker in his contract but they say that isn’t a very big deterrent. The rule called it “trade bonus” which is considered a “Principle” condition.
A trade kicker can not bring a players salary over the max, which is what Ayton will be receiving in year 1 of the deal. So if he's traded and the trade kicker brings his overall payment above the max, the kicker is voided. See the Anthony Davis for an instance where that happened and a trade kicker was voided.
Where the kicker would be in play is in later years because with the cap increasing, he may not be making the "max" any longer. The max he is getting now is 25% of the cap as of the time he signs it and each year after he gets 5% raises. His contract doesn't increase to 25% of the cap each year. Since the cap is likely to increase by more than 5% it would allow enough of a discrepancy for his trade kicker to come into play, which is usually a set percentage like 10-15% increase for that current season.
Also It depends on the language used for who pays the kicker also, sometimes it's the team acquiring team and others it's the team trading him away. Details of that vary.