Does 120/60 meant 60 watts is the limit, or the recommendation?

How would you do this? The wattage that the bulb picks up is based on the design of the bulb itself. Assuming that you are using normal house current, anyway. I suppose if you are running off a higher voltage power supply, then you may be able to “overclock” your lightbulb.

House voltage varies, and can be adjusted by the utility.

You used to be able to get Rough Service/Rural/Farm Use bulbs which were rated at 130V and as a result burned a bit dimmer but lasted much longer.

That sounds like the ones that were sold for use in garage door openers. (I assumed those were designed to handle the vibrations from the garage door.)

Looks like you can still buy them. If you look at the box, it runs for 5400 hours @ 89 W on 120V.

https://www.walmart.com/ip/GE-130-Volt-Light-Bulb/22846088

Like I said, special order. (For light bulbs, anything beyond “picking them up off the shelf while you’re shopping in the store” is special order. If you’re one of those “I buy everything from Amazon” folks, it’s not special but it’s still order.)

Is it possible that the label is actually referring to total wattage for the fixture and wattage for each bulb? Like, a two-bulb fixture intended for use with two 60-W bulbs (120 W total)?

If so that doesn’t make sense given that frequency doesn’t impact on the fixture in any way.

Optimistic I think. The market is not moving towards LED lamps that are made for sufficient longevity to be a fixture.

LEDs requires electronics. It’s unusual to have fixtures that contain electronics.

Umm…
What jail cell have you been confined in?
LED fixtures with non-replaceable lamps are EVERYWHERE. We use them as “pot lights” in our new addition, and as a surface-mount fixture in our bathroom.

Not necessarily. Check this out:

https://www.edn.com/led-bulbs-can-bring-heat/

The LED bulb in the left photo is 15 W, and puts out the same amount of light as a 100 W incandescent bulb. The bulb on the right is an actual 100 W incandescent bulb.

The temperature of the glass envelope near the base of the LED bulb is 160 °F. The temperature of the envelope near the base of the incandescent bulb is 132 °F. Also check out the plot below the photo.

So if the base temperature is of most importance, then an LED bulb might be more dangerous than an incandescent bulb, all else being equal.

Interesting. Thanks! I guess lots of the heat from incandescents radiates out from the bulb.

It’s generally only dangerous to the “bulb” itself.
High temperature kills electronics. Well-made LED A19 base lamps, ones that use either high-temperature electrolytic (or no electrolytics at all) can have lifespans in the 50,000 hour + range. I have a Cree 13W lamp that has been on 24/7 since July of 2013 - over 75,000 hours.

Correct me if I’m wrong, but I have always assumed the maximum wattage rating for a ceiling fan’s light bulb socket (e.g. 60 W) is because the socket can withstand only so much heat. If that’s true, then there may be cases where a 60 W incandescent bulb is fine, but a lower-wattage LED bulb that puts out the same amount of light might exceed the socket’s max temperature rating.

That’s true, but there’s no way that an LED base is going to get at hot as an incandescent that is burned base-up. Remember, the heating element in an Easy-Bake oven was a 60W lamp. If burned base-up, most of that heat is going to end up at the base (being generous, maybe 50% gets radiated away). An LED of equivalent brightness is 13W. Even if 100% of that ends up as heat at the base, it’s still less than 50% of the incandescent.
I’m sure there is a case where someone but some enormous LED in a tiny fixture, and it caused overheating, but the general case is, that the electronics would fail first, before the fixture melted or burned.

So you need an electrician to replace them? Not sure I’d want that. LED’s aren’t as reliable in practice as they can be in theory. It’s certainly possible to run them so they will last near indefinitely, but that often isn’t how they are.

Unless you know what you are doing, yes.
The fixtures are not repairable.
Some of the “can” lights have external power supplies that can be replaced.