Not entirely true.

Quite a few phones these days come with a 'standard' charger that's rated at 5V 1A or 1.5A or whatever and the phone will only draw that.

But, they may support Qualcomm Quickcharge standards despite the phone only coming with a basic 5V USB charger. Quickcharge bumps the voltage up to as much as 20V and current to 3A if you have a compatible charger.

Also there's issues with some phones getting 'confused' by some USB chargers and requiring 'fast charge' cables which essentially just short the two middle pins on a USB cable to convince the charger it's not an old iPhone. The N9 for instance just fails to work with many 'standard' USB chargers and battery packs designed for iDevices. I've still got a couple of dongles that shorted the middle pins that I carried around with me so that I could use other people's chargers.

And lastly, I've lost count of the number of people I know who think any old USB socket is going to be good enough and don't realise that the max draw on some cheap chargers is only 500mA and they've been using one for ages without realising a better charger would help.