Like I say, I do swim "upstream" on at least parts of the project.
If you can pull off instructing your spouse then God Bless You. You will be in a fairly small minority. Having had to personally "pick up the pieces" a couple of times when this didn't work I'm not a fan. But, to each their own.
Seems that learning on a trotting horse has more fans than I thought it would. Another benefit, mentioned by KStinson, is the ability to ride a trotter if you're someplace where gaited horses are not available (like riding vacations in places like Ireland or Spain).
The argument about "speed discontinuity" is bogus, IMO. The rider sets the speed for the horse, not the other way 'round. If a gaited horse rider can't keep their speed down then they need some instruction on properly rating a horse.
I'm still of the opinion that buying a horse for a novice is a bad idea until they've got some lessons under their belt. This gives them a chance to decide if this activity is for them AND it gives them some time to decide what sort of disciplines they might be interested in. It could even come to pass that they want to do something where a gaited horse would not be the best choice. Give the new rider some time to learn what they are about before buying something.
Horses are cheap right now and will be so for a very long time. That means it's easy to buy but tough to sell. Another reason that buying should be put off until the new rider learns what interests them.
Good luck to both of you.