Mechagodzilla’s original purpose in Godzilla vs. Kong could be to fill Kong’s role on Skull Island, which is to deal with the Skullcrawlers. In Kong: Skull Island, Kong was depicted as the region’s self-appointed guardian and he took it upon himself to defend the island from his species’ ancestral enemies, the Skullcrawlers. The Skullcrawlers, who dwelled in the Hollow Earth entry point underneath Skull Island, came out of their hiding places after being accidentally stirred into action by Monarch and the US military.
It would seem that after the events of the movie, Monarch established a more permanent presence on Skull Island by building an outpost there. The credits of Godzilla: King of the Monsters revealed that on top of expanding its forces on the island, Monarch has apparently built a “mechanized giant”. It appears that Monarch’s “mechanized giant” is none other than Mechagodzilla, Godzilla’s robotic counterpart in Toho’s movies. Legendary hasn’t confirmed that the monster is in the movie yet, but his inclusion was spoiled months ago by an action figure leak. Exactly what Mechagodzilla’s role in the story will be is open to speculation for now, but the leading theory is that he’ll force Godzilla and Kong to team up against him.
One of the biggest questions surrounding Mechagodzilla in Godzilla vs. Kong regards the reason for his creation. Some have wondered if he could be their new secret weapon against the Titans in case they ever turn against humanity, but it could be that their intentions for him are on a much smaller scale. Monarch’s plan may be for Mechagodzilla to fight the Skrullcrawlers rather than rely on someone like Kong, who isn't on anybody's side.
Kong would, of course, deal with any Skullcrawlers that come on land, but Monarch may need a more immediate defense for them in case there’s a resurgence. Then there’s the matter of Monarch’s next mission in the MonsterVerse, which is to explore the Hollow Earth tunnels beneath Skull Island. It doesn’t seem possible for Monarch to safely undertake such a dangerous task, knowing that the Skullcrawlers reside in those tunnels. Monarch will be fully aware of the danger they pose, and will need an answer for them. Kong, who is unlikely to go down there without proper cause, can’t be depended on to clear the way for them, so a different weapon will likely be needed. Since the tunnels are large enough to allow for Titans to traverse through them, Mechagodzilla could be used as their source of protection (and transportation) in the Hollow Earth.
As for why Monarch would model their weapon against the Skullcrawlers after Godzilla rather than Kong, it could be that they identified Godzilla as the perfect predator, and they may have wanted a robot who emulates his best qualities. Plus, his ancestor’s skeleton from the 2014 movie could have provided an excellent blueprint for a powerful, manmade Titan. The problem that may face Monarch though, is that the Titan they created may be too powerful. If he gets hijacked by Godzilla vs. Kong’s human villains, Mechagodzilla may turn his attention from the Skullcrawlers and focus on killing all the Titans in the MonsterVerse.
