Does Your Toddler Love to PUSH Things?

Totally normal. ;)
My son (same age) has one goal in mind every day...get himself outside to push his cozy coupe around the block. Lol!
And his new goal when we are out shopping in to get out of the cart so he can "push" it on the bottom basket bar. : /
My DD's favorite toy at this age was her shopping cart. (He loves it too.)
HTH!
To your SWH: We had to put the wagon away for that reason-DS would climb out to push. My DD (who your stories of your son remind me of) would not sit in a stroller until she was nearly 2.
He'll get there. ;)

Yes, this is a normal stage, It is easier to push than to ride and make the legs work one at a time in an order.. Many times when they first ride they can only go backwards! soon he will want to ride them..

Even a cardboard box toddlers will push them all over. the place.. .

A couple of my kids did that for a while. They were just into pushing. It's a great, grown-up activity! After a while they discovered the joys of riding. It's OK.

All of my kids were like that. Some kids develop in different areas than other kids.