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That's an interesting angle.  My first reaction was "I fucking hate Ted Cruz but this might be good".  Now I wonder if I'm falling victim to thinking the grass is always greener.
Wouldn’t he be one of them? >

On the contrary. 
Accepting any grandfather clause that has been mentioned, term limits precisely benefit unpleasant social climbers like Ted cruz. 
Congress is very much a traditional institution and Leadership roles are often very heavily determined by seniority. 
Mitch McConnell is a skilled politician. But Mitch McConnell is also Mitch McConnell because he's been in the Senate since 1985.   
If you impose term limit of say two consecutive six-year terms.  Every new election cycle you'd have an argument about who among the most senior senators are qualified to be the majority leader. 
A self promoter like Ted Cruz thinks he could benefit from that.