To know what the opponent plays with is the most common reason. It happens that a player will never use one of their rubbers during warmup and hope that the other player doesn't notice it until the first points. Can be surprising if the rubber is "unusual": pips, antispin, etc.
It also allows you to get to know the different brands and types of rubbers if you are interested in that.
The same applies to the blade: if you see an All- or an Off+ the difference is huge.
Regulations do come into play but should be enforced by the umpire and referees when you have some. Since players don't usually go around with the List of Authorized Racket Coverings, they will mostly look for missing parts of rubbers or more blatant misbehaves (I've seen a player trying to play with 2 red rubbers once).
The list of authorized blades doesn't exist, hence you can play with virtually anything made out of wood, as long as your rubbers are authorized and cover all the blade, which means that theoretically you can have a racket as big as the table, whereas in tennis and badminton the racket size is limited, so it really depends of what you call "stricter". Also worth noting: you can play with only one rubber if you want, and win the Olympic Games this way if you are Ryu Seung-min.