Three possible methods...
Count pulses from meter in PLC.
Integrate analog signal from meter in PLC.
Communicate serially to totalizer in meter from PLC.
All of them work. All of them have advantages and disadvantages.
Count pulses works great if you want a total, not so great if you want flowrate. All arguments about missing counts, wiring noise are missing the point. Do it right it works, do it wrong and it doesn't. Just because you have seen it done wrong doesn't mean you should never use it.
Integrate analog signal. This one has limitations. The first one is, the accuracy of the analog signal itself. The second is the basic assumption that the flow is constant between samples. For example, this method always indicates low when the flow is ramping up, and indicates high when it is ramping down. There are techniques to eliminate the round off error you get with large floating point + small floating point. That's not a big deal if you do it right.
Serial communication to the flowmeter's internal totalizer. More difficult to implement, but easily the best all around. You have the full accuracy of the meter. No added error in signal conversion. You get to take advantage of features in the meter that would be difficult to implement in the PLC. Empty meter detection for one. In the case of mass flowmeters, the volumetric flow is based on the density at the time of sample, very difficult to do in the PLC. And it's the only way the local display and the PLC will ever match.
Any one of them may be the "appropriate choice" for an application. It depends on the requirements and the budget.