Hi Michalis, & welcome aboard Rollaclub !
There are a lot of things on a car, that if they break down; don't stop You from getting from point "A" to point "B". Windscreen wipers, headlights, a horn; or even an reverse gear; don't have You broken down on the side of the road, & isolated, & going nowhere.
However, the engine is paramount; closely followed by the alternator. Even with a fully charged battery, if the alternator fails; it won't be that long, before the engine comes to a stop, on the side of the road.
The "electrical loads" on a battery, have only increased, over the years, as we add more & more electrically powered devices & gadgets to our cars. There are ways, in which You can decrease the electrical load on your car, by say . . . . . "converting all light bulbs to LED ones". I did this in the past couple of years, & it was a really good upgrade. Brighter lights; less voltage drops; & lower power consumed.
When our Corollas were first built, the alternators fitted were pretty standard, & produced 30-35A maximum, at their output terminals. Invariably, the early ones had an external "voltage regulator", that consisted of relays that vibrated to produce an excitation current to the alternator. Later ones, like the Bosch one, you imaged; had a solid state regulator, built into alternator body, & very easily replaced.
Alternators have improved dramatically over the last decade or so, & alternators of similar size, to the ones You depict, can now produce outputs of 80-120 amperes.
I purchased an alternator on line, that was cheaper than an new replacement, exactly the same as the original fitted to the car. It produces 120 amperes output max.
120 Ampere rated alternator fitted to my 5K engine
It was the best upgrade I've done, of recent years.
The single biggest wearing item, in the alternators, You've depicted is the commutator. These wear & get "out of round", & result in more rapid wear of the carbon brushes.
I would strongly suggest opening the alternator up, & inspection, commutator & brushes, before fitting a second hand unit to your car.
Another alternative, is to find a second hand alternator, with greater output, that will fit. Years ago, I purchased a reconditioned alternator, from a Toyota Hilux utility, that produced about 65 amperes max. Off memory, it only requires a couple of washers, on the mounting bracket bolt, so that the pulley at the front lined up perfectly.
Hope that these suggestions assist. Good Luck !
Cheers Banjo