more often than not, high power LEDs seem to be primarily categorized by their wattage. Why is this the standard?
People keep doing stupid things because their predecessors did stupid things and they expect other people to be confused if they stop doing stupid things.
It dates from the days when light was produced as an inefficient tiny side effect of heating tungsten filaments almost to their melting point. At that time the amount of power consumed or heat produced was a rough analogue of the amount of light produced because there were few alternative technologies in general contemporary use. The general public became familiar with the amount of light expected from a 15, 40, 60 or 100 watt incandescent tungsten-filament light-bulb. Maybe the majority of people encountered and understood watts more than candela or lumens.
To confuse their customers.
See "music power". Manufacturers of inefficient products like to hide that inefficiency. Thus they promote watts as if it were a virtue and hide luminous flux (lumens), lumens per watt, illuminance and other more useful measures.
Don't get me wrong, power consumption is an important piece of information - but it shouldn't be the primary characteristic of a light source.
It has been suggested that, in the context of wiring up lights in a house, watts are the most important characteristic. This is not so.
Many years ago, when I moved into my new house, the electrician had provided light bulbs in every socket. Since these were mostly 60 watt incandescents and not not 15 watt fridge bulbs I can tell that power consumption was not the primary selection criteria.
Like almost all UK houses, mine has a 6A lighting circuit for all lights on the ground floor. That is standard. The electrician who wired up that circuit followed the general standard and gave no thought at all to the wattage of bulbs that might be used. Nor should they.
That circuit has 10 light sockets, the kitchen has additional under-cabinet lighting but I'm pretty sure those come off a separate circuit. But lets include them anyway and pretend I have 15 sockets where the householder can insert a light-bulb.
If I go to a supermarket today, the most powerful light bulb I can buy is 12 watts. I would need to fit 70 of those to my 15 light-sockets to approach the rating of the circuit. Clearly the power rating of typical domestic light-bulbs is irrelevant.
Electricians are in fact much more concerned with amps than watts. Indeed bulbs now often have both marked on them. UK klighting circuits are 230 volts nominal (EU standard) though usually 240 volts in practice (old UK standard). I looked at one light bulb which was marked 12 watts, 85 mA. If you do the sums you'll see the electrician can't use the watts to check load on circuit accurately. Clearly there are complicating factors in the driver - power factors, inrush current for a capacitor or some other reason. The electrician should disregard the power rating in watts and use the current rating in amps.
As I said, when I moved into my new home, there were light fittings and light-bulbs already in place. There were no lamp-shades - these were regarded as a purely decorative item that the new owner should select themselves. But it is the lampshade's ability to handle heat that is the only time you need to refer to power consumption of the bulb. Lamp shades are marked with a power rating (e.g. "40W max").
However currently it is not possible to buy, from my nearest supermarket, a light-bulb that will approach even 40 watts. So this is, for me at least, also a non-issue nowadays.
As a final piece of evidence of this stupidity I offer the following
This is one of the least egregious examples, many such items omitted the actual power rating or had it in tiny print on the other side.
I hope I do not have to explain the gross stupidity of what is shown above.
When selecting a device whose sole purpose is to produce light, its most important selection criteria is, in fact, the quality and quantity of light it produces.
In a domestic context, meeting a current budget is a secondary consideration and in most cases totally inconsequential. Most lighting circuits are grossly over-specified for todays high-efficiency lighting.
When choosing a light source for a fitting where heat dissipation is an issue, power ratings are important. This is almost never an issue in a household context with LEDs in fittings designed for incandescents. But in any case it is third on my list, not first.