I don't see the police having to fight tanks and bigger things either, but well.
Real life examples... so... unrealistic.
This is the part that people always get wrong.
The LPI, the LN and the LSF are the three part of the same organization, they are Liberty's defense, this is not real life, stop trying to compare to real life, because it's stupid, starting that we don't live in space, we don't have asteroid fields with hiden pirate bases were space cruisers and gunboats hide. If you really want to compare this game to real life, you have to take a country on civil war, were both sides have heavy weaponry, and police barely exists, it's the Army protecting the streets.
So, if you think on it a bit, the LPI is like the patrolling arm of Liberty's defenses, and eventually they got to fight gunboats and cruisers, and liberators are not the best ship to deal with those.
Depending on the situation LFs are better than VHFs, problem is, the majority of time, there is no use for LFs, and situations change so fast from stopping a transport to shooting a cruiser, than the best suitable ship for the job is the VHF, or a bomber.