Is it true that there's no advantage in filing patents to each major patent office rather than filing it through the PCT system?

The patents, once granted, are equally valid and enforceable in each country regardless of the path taken.

There can be a cost saving if the applicant knows early in the process where they need to file and it is a small number of places. Each country's charges are typically a little less via the PCT but you have the PCT cost itself as "overhead". It is often estimated that for only two places, direct (under the Paris Convention) would be less expensive. You can look up the filing fees and calculate it.

You have some control over the costs. When you file a PCT application you chose an ISA (International Search Authority) to do a search. The cost of having the U.S. or the EPO as ISA can be significantly greater than Korea or Russia. The PCT process does not obviate actual substantive examination in each country under that country's criteria and system.

One can also get earlier allowances by filing directly. The PCT process lets you delay deciding where to actually file - that is a plus unless you know where you want to go. There are also regional entities like the EPO that allow one filing that can end up with multiple patents in any of the EPO countries. If you do not know where you want to go but definitely know it is only Europe, filing directly with the EPO buys you time, as the PCT does.

Of course you can go to the EPO via a PCT filing. Unlike the PCT process, an allowance by the EPO gets you national patents with no further ado, other than paying money.

Another benefit of PCT filing if you are thinking of filing many places is you get an International Search Report before you actually start spending money in specific places. You might get an unpleasant surprise if the ISA digs up some killer prior art. You might decide to drop the application.

In about 1999 a top patent firm filed an application for my company. At that time the PCT was relatively new and they chose not to use it to avoid risk. That is in the distant past.