I am not a "Purist" but there are combinations that are unsafe, or reduce safe a proper handling.
On most stock bikes, the rim width is the minimum width, or to say it another way, the largest width tire that the rim will accept.
I can give you an example. My CB360, stock, comes with a WM1 (1.60 inch width) front and a WM2 (1.85 inch width)rear. The front has a 3.00x18 tire and the rear a 3.50x18 tire.
If you look at the chart, the 3.00 is the largest tire width recommended for a WM1. On the rear, the 3.50x18 tire is the widest recommended for a WM2.
Whe I restored my CB360, I bought a WM2 rim for the front and a WM3 rim for the rear. I re-laced the wheels with Stanless Spokes from Buchanans.
I am still using stock tire sizes on my bike. With the wider rims and stock tire size, the handling on the bike has actually improved. The sidewalls are less pinched in and hacve stiffer resistance to side force bending.
To go wider, you have to make sure the fork/swingarm have enough clearance.
The problem is most people do not put wider rims on, but just wider tires. Wide tires on under-width rims reduce safety and handling because the tire will deflect more because the sidewalls are pinched in. Even though many say the ride fine with them, to me that means they are unaware of the handling characteristics and don't know what proper handling for the bike feels like. Putting wider rims is the correct way to improve handling and allow safer use of wider tires if desired. In addition, wider tires, even on proper rims, slow handling. It takes more handlebar force to initiate a turn, making the handle like a heavier bike.... Motorcycle with really wide tires need to change rake and trail and chassis geometry to compensate for this.
For an older bike, the stock tire sizes are generally the best size for good handling and ride. Fatter tires reduce the handling, slow the handling down. This is not opinion, it is fact. As long as you know the effects and consequences, you can do whatever you want....