It may sound strange to a traditionalist, but once you give it a try, I bet you will not only like the texture, but appreciate the easiness of it as well.
I have a large family (2 kids 100%of the time, 4 kids 50% of the time) so making food that's easy to prep and quick to reach their chatty, little, hungry mouths is a win-win for me. I adapted a recipe from a traditional Mexican burrito into a Californian cuisine style burrito that gets warmed up and crunchy while sitting in between a panini machine leaving my hands free for rolling more burritos till we have enough.
The standards are in it; meat, cheese & beans. But I add finely chopped veggies like, bell pepper, onions, zucchini, chilis and/or corn. Plus, cooked quinoa instead of rice keeps it healthier and light. After we eat it this way, we do not feel that "food baby" or the heavy feeling a burrito can often give, ruining your ability to walk for a while, which is welcome unless you're hungover and still need to sleep it off.
My tips are to try and have your filling already warmed up in a pan before filling/rolling the burritos because the panini machine won't be able to warm it all the way through without burning the outside of the tortilla first. And if you want melted cheese in it, make sure the cheese it closest to the tortilla instead of in the middle of the burrito itself. Sour cream, avocado and hot sauce obviously aid in the amount of "MMM's" you hear.
Give it a try. Make it your own by choosing ingredients that you and your family or guests prefer.