I guesss I'll answer this for the Smogon tiers.
Currently, Urshifu-Rapid is banned in Generation 9 OU, but it is not banned in Generation 8 OU or National Dex. I'll start with Gen 8 first (my knowledge may be flawed as it has been some time since I've played.)
Urshifu-Rapid suffers a lot more from various contact abilities and items. Due to Surging Strikes hitting three times, Urshifu-Rapid is prone to getting chipped down from the likes of Iron Barbs (Rocky Helmet) Ferrothorn, Rocky Helmet Toxapex, and Rough Skin (Rocky Helmet) Garchomp, along with increased Paralysis chance from Zapdos's Static. Yes, it can run Protective Pads, but then it's not getting as much damage as Choice Band sets or enough speed as Choice Scarf sets. Speaking of the Choice sets, locking Urshifu into one move gives opposing Pokemon extra opportunities. For example, an Urshifu-Rapid locked into Surging Strikes has to switch against, say, a Rocky Helmet Slowbro, who can then Teleport after Urshifu's teammate has switched in and thus gaining momentum. An Urshifu locked into Close Combat gives Giga Drain Volcarona a free setup opportunity. This isn't to say Urshifu-Rapid is bad, it's just that Urshifu-Single did not have to contend with the contact-punishing issue that Rapid has to deal with (plus Dark is a much more spammable STAB against the likes of Pex, Ferrothorn, Volcarona, and so on.) Urshifu-Rapid is actually a great Pokemon, using it's three viable items to potentially bluff one while using another, along with packing Aqua Jet for realiable revenge killing on non-Scarf sets.
Now onto National Dex. Before the Tera Ban a while back, Urshifu-Rapid is considered a premier offensive pick. Although it basically ran Choice Scarf 90% of the time, it's so scary that people just used it. As an example, Tera Water Surging Strikes OHKOs Mega Charizard Y under Sun. Scarf Urshifu oustpeeds a ton of common Pokemon and even some considered to be speed control, like Mega Diancie, Mega Lopunny, Scarf Tapu Lele, and Scarf Landorus-T. However, being essentially into Choice Scarf has its downsides. Without Scarf, Urshifu will stand nary a chance against all the aforementioned Pokemon that now outspeeds it, as well as Mega Charizard Y with its Solar Beam. With Scarf, although Urshifu-Rapid can use U-Turn to scout switchins, the prevalence of Volcarona, Zapdos, and Moltres means it is very likely Urshifu-Rapid will get statused at some point. Some Pokemon, like Double Dance Booster Iron Crown and Choice Scarf Kartana, also outspeed Scarf Urshifu and have options to OHKO it. Thus, Urshifu-Rapid was a top pick in many teams, but it was controlled by common counterplay options. However, after the Tera Ban, Urshifu-Rapid's usage dropped off a cliff. Most of it is due to the return of previously banned monsters, like Dragapult and Zamazenta. Dragapult resists both of Urshifu's STABs and can use it as setup fodder if locked into Surging Strikes, while Zamazenta can set up Iron Defenses and is bulky enough to live two Surging Strikes with common Body Press sets. There is also the elephant in the room: no more Tera Water Surging Strikes that are absurdly powerful for a Choice Scarf Pokemon. This isn't to say nobody is using Urshifu; Swords Dance sets have popped up lately, as it can break Melmetal while being a great Kingambit check. It is worthy to note that the metagame is still developing; with Pokemon like Dragonite and Ogerpon-Wellspring losing usage, Scarf Urshifu may climb back up as a premier threat. However, with how useless it is against Dragapult (unless you switch it in before a Speed boost from Dragon Dance or a Will-O-Wisp from status sets and use Ice Spinner), Urshifu-Rapid may still be good, but definitely not as great as before.
Hope I helped!
