Increasing cop presence won't fix that problem. In multiple jurisdictions, cops can also refer you to be involuntarily committed.
So we're not creating an extra judicial system that has no checks and balances, that system already exists and cops are a part of it. We're talking about the potential benefits of removing one harmful part of the equation. If you want to also talk about the negatives of involuntary commitment and make progress in that area, that's totally worth examining as well, but it's not an argument for flooding the streets with more cops.
Getting arrested doesn't mean you can't be involuntarily committed afterwards.
Also note that in some cases, getting arrested and thrown in a holding cell can on its own be just as traumatic of an event as being held for an involuntary mental evaluation -- particularly if someone is genuinely suffering from a mental attack. And arrests don't require trials either. A sizable portion of the people in our jails have never been convicted of crimes, they're just stuck there because they can't pay cash bail.