I don't believe that having language included excluding the use of another franchise tag is an unreasonable ask by Prescott and his people. Nor is asking for the inclusion of a no trade clause as well.
If he is "your" guy, commit to him. They have played their hand regarding him since his rookie year. So, as long as the numbers are reasonable enough to still have room to field a talented team around him, and the years are agreeable enabling the team to spread his cap hit...add the language and get it over with. If he isn't your guy...tag and trade him and move on.
As an aside, knowing he wants this language leads me to presume that Prescott won't budge on wanting a shorter deal so he can test the market again sooner rather than later.