I'm someone that loves systems when they're done well, and my last few sites have had systems. I thought I'd offer my perspective as someone that loves designing and using these things.

If you have to ask yourself whether or not you should have a system, the answer is almost universally no. They'll end up tacked on and just kind of bad. I know there are a lot of Pokemon sites out there with systems, but that's also kind of the point here. If someone wants a Pokemon site with systems, they already have plenty of options. If you want your site to just be freeform, it means the people that want Pokemon, but don't want to deal with systems have a place to go now. It doesn't mean you can't have some combat guidelines to make sure everyone's on the same page (eg general etiquette guidelines for dodging, using the wiki for a general guideline of how strong you should expect attacks to be relative to each other, or whatever else), but you don't need more than guidelines for that kind of thing.

This is at least the impression I get from your OP. I think this only answers half the question though, so I'm going to go into when systems should be used and what they're good for. This is all just my opinion based on my experiences with systems.

It's important to remember that RP is not video games. The mediums and the goals of each medium are very different. Video games want to take you through an experience crafted by their developers and mechanics, whereas RP is about collaborative writing and creating a story with a group of people. Thus, people shouldn't necessarily look to video games when creating systems. They can make good inspiration, but ultimately the goals of the two mediums are very different.

So what does this mean for RP systems? It means they should focus on helping players create a narrative. They should exist to help people agree on an outcome so the story can move forward. This will ultimately mean sacrificing a little bit of their narrative control when compared to freeform, but in exchange they can be surprised by outcomes (because in freeoform players decide everything and thus are limited to what they and their partners think of, whereas systems can effectively provide writing prompts and scenarios they may never have thought of themselves), and be on the same page as their fellow roleplayers (so people won't go raid the same warehouse 50 million times while the organization that owns them feels 0 effects).

This is where I think most tier systems fail. They don't make any kind of resolution system, so they still rely on entirely freeform combat and RP, only giving people a more rigid structure for what a text description could provide. People just seem afraid to let go of that narrative control that freeform provides, but still want to put numbers on things to keep combat 'fair' or to head off troublemakers, which results in the worst of both world: adding just enough structure to limit peoples' ideas, while also not giving that sense of surprise and direction that systems can provide.

So that's my two cents on systems. Since the system should imo, help determine the direction your site's story will take, it's just as important as your site's setting. I would even go as far as to say it's a different way to define your site's setting. So if you're asking if you should tack a system onto your site, that's pretty much always going to get a no from me. If you want to be freeform, be freeform. There is absolutely nothing wrong with freeform.