You always have to be prepared to move, can’t change stuff without landlords approval, can’t buy nice stuff (good luck moving your 80 inch TV with your nice leather couch).
There's benefits to renting too, you have to make the right choice for yourself.
The point is that financially we expect that two approaches to be comparable, perhaps with renters paying a bit for that flexibility and shorter term commitment. (That they aren’t over a particular period is fortunate for those that managed to time the market).
I suppose if you account for this extra cost (which may be non-monetary, but one can always assign the inconvenience using a dollar figure...) then renting could be worse off.
it is possible to make a guess at the monetary value of these advantages, by comparing the difference between the cost of renting vs cost of owning (including cost of capital). Of course, the value of owning is different between different people (some might prefer renting due to the flexibility of moving at a moments' notice for example).
And in fact, if it turns out that owning is lower cost in total (even taking into account the cost of capital), then it would make a lot of sense to buy! And in some areas, this is definitely true.
The OP said their mortgage is already lower than rent, which is typical, so it is the homeowner who has extra money left over (compared to if they were renting) to invest every month. The renter has ever-increasing rent swallowing up any raises, so not much left over to invest.