As someone from the '1 GFCI for the entire house' countries, i can say that it's not that big of a deal. Years go by without the thing ever tripping. It's so rare that i actually remember most of the trips:

- Central heating burner was not cleaned properly causing flames to lick past some sheet metal which deformed and contacted a live contact, causing a short to ground (around 2018)
- Faulty ATX power supply (2001, likely an actual nuisance trip due to a 'weird' filter, but a different PSU solved the issue)
- Faulty bread making machine heating element (2024)
- Faulty door hinge support of an oven, which over time wore through a wire (2015, different house)
- Ants crawling inside outdoor lights causing leakage to ground (2023, stationary caravan)
- I think once or twice in 30 years it tripped from a very nearby lightning strike.

Code now requires or recommends the lighting in new houses to be divided over multiple GFCIs so if it trips, you're not in an entirely dark house. But even if you're on a single one, it's not that big of a deal when the thing trips. You grab your phone or a flashlight, turn off all breakers, turn on the gfci and turn on the breakers one by one and see on which circuit the fault is.

My brother who is an electrician with 21 years experience had to replace a Square D QO GFCI breaker in our house that often tripped for no reason reason whatsoever. There wasn't anything even plugged into the outlets when it would trip. He said often times GFCIs can trip inadvertently because of long wire runs. In this case the original electricians for the house spliced 4 outlets together in the panel and tied the splice to the breaker. Then the wires ran in 4 different directions 2 bathroom outlets, 1 in the garage, and finally 1 on the patio. Now the house was built in 1978, so naturally the codes were different.

That is a classic moisture intrusion fault. Patio - outside, insects, moisture. Bathroom - moisture. Been there, done that (ant intrusion).
Megger that circuit.

GFCIs should not just trip by themselves. They really don't do such things unless they're broken (and they can get more sensitive over the course of 2 or 3 decades).
The only thing that long wires have a lot of influence on, is causing triggers when lightning strikes nearby.

Must have been an issue with the breaker itself. Once a replacement was installed everything was fine again. I guess it was just going bad or just was more sensitive from age. I often wonder is better to have a GFCI breaker or a standard breaker with individual GFCI outlets 

There is a problem with long wiring and cheap very sensitive GFCI's: The wire capacitance on longer wires creates current imbalance, which may be misinterpreted by the GFCI as a ground fault. Mainly when transients are present on the mains voltage, like those originating from switching og high currents, mainly things like AC compressors or so. These spikes, when driving longer cables (-150pF/m, so in nF for 10m wiring) can easily exceed 100mA peaks. If the GFCI does not include any filtering, nor any other discrimination, it could be parasitically triggered by that. Mainly the case for very cheap "still according to code" devices suffer the most, as it takes extra engineering and manufacturing precission to set the triggering mechanism right.
There is a reason, why the standards allow certain response time for GFCI, as a function of the fault current. And why the fault current the GFCIs are supposed to respond is described as purely resistive (the low levels, below 60mA, for single phase GFCIs).
And why decent GFCIs really use that time window to respond and why they are that "picky" on the fault current phase at the low current levels.

Must have been an issue with the breaker itself. Once a replacement was installed everything was fine again. I guess it was just going bad or just was more sensitive from age. I often wonder is better to have a GFCI breaker or a standard breaker with individual GFCI outlets 

The best compromise is something that's called an 'Alamat' here - a combined GFCI and conventional circuit breaker in 1 device. That means that every circuit is ground fault protected, and you can use conventional outlets.
But we still often use 1 GFCI per 3 circuits, simply for cost reasons.

It all depends on local electrical code as well as your personal wishes. The more GFCIs you use, the lower the trip current can be, but the higher the cost.

I'm not too enthousiastic about only having a gfci inside each outlet, because that does not protect the wire runs themselves. In other words, if you drill into a power line, you can get zapped without the GFCI ever knowing about it. Same with moisture intrusion into junction boxes. Power won't shut off even if the wires are practically submerged, but if they dry out and damage is done, you can have arcing with the associated fire risks.
An AFCI can protect against that, but ideally you catch the problem before arcing starts.

I had once problem with tripping RCBO breaker (combined circuit breaker with RCD/GFCI), this was caused by flow water heater located on the sink tap under garden bower, problem was solved by water heater check, neutral wire from power cord was loosen and some current flows into ground probe in the heating section.
Luckily here we have few RCDs, not one for all and only one socket circuit from the bower was disconnected due RCD trip