While many people fully expect the shichibukai to stomp in their upcoming clash with the marines, I'm not so sure of this. Kaido himself stated that the marines hadn't lost their minds when they replaced the shichibukai, meaning that the SSG has to be strong. Hence, it doesn't make sense for Oda to hypetool the SSG when they don't have any feats yet.
The marines are one of the biggest enemies in the series, hence Oda actually needs to hype up the SSG, moreso than he needs to hype Mihawk, who has already received more than enough hype throughout the series.
Another thing is that Mihawk is a very important character and post-wano, we will be very close to the EoS. Hence, Oda needs to get MIhawk back into the main plot. In order to do this, Mihawk can't just be sitting on his island like he has for a majority of the series. The only way for him to leave would be if he was driven out by the marines.
I suspect that the marines have sent an admiral and/or members of the SSG, to Mihawk's island. In this fight, Mihawk will be overwhelmed, become injured, and ultimately run away from the marines. Through this loss, Mihawk will either find himself allying with shanks or somehow interacting with blackbeard.
Also, an important thing to note here is that the SSG doesn't actually need anyone on par with Mihawk in order to defeat him. Multiple high tiers, if they are strong enough(say marco level), could be enough to pressure mihawk.
