In child care little ones go through stages like this. Here's what we'd do to get them to go to sleep.
We'd darken the room at least 80%.
Play classical music very softly, or something soothing and instrumental.
Sit by their cot and gently pat or rub their back.
Consistently put them back on the mat no matter how much they resisted...not in a mean way, just took them back to their cot.
Had a routine after lunch where they ate, cleaned up, got a diaper change, washed hands, went straight to their cots, no playing, no TV time, no toys, nothing but straight to their area that is ALREADY dark, music is already playing softly, etc...this routine got them mentally ready.
Kids go through stages like this and we have to keep them napping as long as possible. Our bodies wear out and sometimes we just don't know that we're tired enough to take a nap. When we're sleeping our brain/body doesn't have to process so much and they can work to do other things. Heal our body, fight off disease, grow...little kids grow a lot when they sleep, and many other things.
We have to have sleep or we get run down, sick, and more.
My main reason for insisting my grand kids nap is that they have to lay down at school and have a rest/nap time clear through Winter Break in Kindergarten. If they go to Pre-K they'll lay down and have nap time. If they aren't taking a nap anymore or at least still having lay down and rest time they have to relearn to do that.
I understand that lots of kids decide they don't need a nap anymore but I have always been able to change that by just being consistent and making them go to their cot/bed and lay down then pretty soon they're back in the habit.