I am quite ignorant to ships, not being intereste din them since the battle of Jutland and the introduction of the airctaft ruining the wargame beauty of them, so correct me if I am wrong:
The great advantage of small ships here is that they are basically MUCH cheaper to build (a big one costs like 10x the cost of a small one, let alone an aircraft carrier) and *especially* to operate. Lower fuel, lower personnel.
In 99% of cases the big maritime power of the world (USN)is using flotillas for the big stuff. The thing is, the big stuff is strategic, not really operational 99% of the time. The flotillas do not really engage other flotillas because there are none around, or they are scarce. So, they end up being the mobile bases to provide support to your ground pounders around the world.
For shore activity a small ship or 2 acring alone is more than enough if the enemy does not have cruise missiles or potent aircraft (remember, I am pre-WW2 mentality here). So to show the flag and bombard a pair of residential districts to make the target comply a small ship is enough. so is it to detain pirates operating in skiffs and coastal boats that assault the supertankers going around. I know that Spain sent a frigate to do that in Somalia (pirates were kidnapping Spanish fishermen ships) around 2015 and it was plenty successful.
In general having a lot of big ships is OK, but it might be overkill, dunno. 300 military ships in a navy certainly sound like a lot to my untrained eyes!
I am probably ranting now, so I will stop.
Ok, without straying into Rule 4 territory, the short answer is no, to all of it. *Wall of text warning*
The warfare theories underpinning warships are perhaps the second most complex, behind only infantry. There are between three and ten warfare domains for a warship, depending on what doctrine you're reading, and multiple roles within each of those domains.
The primary advantage of smaller ships is they are generally more easily specialised, with additional advantages in cost of manufacture and maintenance, crew sizes and simplicity of logistic support.
The primary advantage of larger ships is that they are simply better at their role, be they primary or secondary, by virtue of having more space and weight for the equipment necessary requiring less compromise in design, secondary benefits are larger crew sizes and space available generally mean longer endurance while conducting activities, and consequently greater ability to undertake multiple tasks simultaneously.
Generally speaking, navies will want to use the smallest ship practical to achieve their mission objectives, and the size with the greatest efficiency is in the frigate/destroyer range, which is why most navies build exclusively these. Larger ships are more expensive and complex to operate, but can project power much more effectively and generally will be much better at preventing escalation. In order to be considered a world leading navy, you need big ships, and thus need to be willing to spend a lot of time, money and effort on them. These larger ships don't simply sit idle, they are used to project power, and frequently will be used in support of smaller vessels undertaking the tactical tasking, providing that big brother protection and preventing adventurism from the target of the tactical action or third parties. Think about it like an altercation with police hanging around just a short distance away, they keep things civil.
As for using small ships in close to shore, without that back up, that's not a good idea at all. Weapons to at least mission kill small ships are relatively cheap and quite prolific, sending small vessels in to enforce your will without support from larger combattants or aircraft, makes it likely you will lose one or both, not a palatable option.
