Maybe the age is a factor here. Most youth sports start (in US) at elementary school age. I think for badminton to gain popularity, young kids (7-8 olds) need to start playing it. At this age, I honestly think tennis requires a lot more to play. They make soft tennis balls for young kids for this reason.
Again we are talking about popularizing the sport… I honestly don’t think “difficult to play” is a factor here. Most kids at my clubs start at 7/8 age and the skill progression is quite natural.
Well, I don't know much about either sport in that age bracket.. But, I know that tennis can be practised very well against a wall.. I can play tennis against a wall, and my tennis is very beginner level. Whereas badminton against a wall, i've found it very hard! I've seen coaches do badminton against a wall, and even then they can't do a really long rally. In tennis, a wall works so well it's like a coach feeding it back. A 7/8 year old could do tennis against a wall..
In tennis from what I have googled, the commonly stated reason for the different type of ball for children, is that regular balls bounce too high relative to their height. So by that reasoning, different type of ball will make it more realistic to adult tennis.
I reckon tennis by children with a ball that bounces less high, resembles proper tennis far moreso than "to me to you" badminton being done by 7/8 year olds resembles proper badminton. 'cos coaches try to coach people out of "to me to you" badminton. I really don't buy the badminton is easier argument, for any age.
And I think tennis has other arguments in its favour over badminton e.g. I don't think the heart rate goes quite as high so I think it's healthier for the heart.. Badminton is very stop and start.. Tennis is I think more natural for the cardiovascular system to get into.
But, I think there may well be arguments for where badminton is better than tennis..
If it's "To me to you" badminton.. it's fun..and good cardio.. Could be more enjoyable than tennis there.. (though coaches come and coach that style of badminton out by showing how to punish bad shots! And "to me to you" badminton is not a thing at club level and upwards)
Also
At an advanced level, it's a very beautiful sport, the movement is so unique and unusual. BWF do it a disservice with their bad videos and not only that but their copyright policies preventing other people from clipping any part of their videos for other person or not BWF youtube channels.
It's a complex remarkable sport, it's hard to cover a whole court, learning the footwork.. A person can easily be inspired by how beautifully the top players move. And wanting to be able to do that. (Not being inspired by trickshots 'cos that's not what badminton is all about,.. the people that can do trickshots, have trained over 99% other things, so somebody getting into badminton for the trickshots is a false sale!).
And the fact that it has power shots and delicate shots and precision..all mixed together.. it's a very technically interesting game.. (though with the tendency of most people to skip over technicalities, maybe may as well do tennis ;-) )