Probably rule bending nonsense, but I found this an interesting loophole for a multiclass build concerning Cleric subclass' Divine Strike:

Divine Strike

At 8th level, you gain the ability to infuse your weapon strikes with poison — a gift from your deity. Once on each of your turns when you hit a creature with a weapon attack, you can cause the attack to deal an extra 1d8 poison damage to the target. When you reach 14th level, the extra damage increases to 2d8.

Unlike Fighter's Extra Attack, this doesn't specify that you must reach 14th level in the cleric class specifically for it to upgrade to 2d8. 

I think this is just a silly reading depending on RAW rather than intent, but It could make an 8 level dip into certain cleric subclasses even better for a monk or rogue. 

What do you think? Would you allow this at your table? Is it far from broken? 

A lot of class and subclass abilities are written that way (e.g., improved combat superiority, magical secrets). Taken to the extreme, you'd only need to take a subclass to gain all of its abilities. For example, roguish archetype says "your archetype choice grants you features at 3rd level and then again at 9th, 13th, and 17th level."

Class features must be reach a level in their respective class for you to gain the benefit so the feature Divine Strike extra damage increases to 2d8 when you reach level 14  as a Cleric. 

Class Features: When you gain a new level in a class, you get its features for that level. 

Class features refer to Class levels. This is because the base rules suppose a single-class character, since multiclassing, despite popularity, is an optional rule not a base one.

If i am not mistaken Divine Strike is not even a Cleric Class feature, its. Divine Domain feature  so you absolutely need to have accumulated enought level As a Cleric of that Domain to get it.

Devil’s advocate: cantrips are learned via a class feature (spell casting) and scale even if you only take a single level in that class.

and most expanding features like this do note a class requirement in leveling, because multi-classing was accounted for in the basic rules.

Quote from Kronzypantz >>

Devil’s advocate: cantrips are learned via a class feature (spell casting) and scale even if you only take a single level in that class.

 
Spells themselves have their own separate rules. Class features may grant access to spells but spells themselves are defined outside of class in the Spellcasting chapter - their own set of rules. As such they hold no context of class levels in and of themselves and so can, indeed, scale by character level unless otherwise stated : so in general, cantrips scale by character level and spells of 1st or higher level scale by spell slot level. Exceptions apply, of course, but this is why cantrips/spells are different than class features, even when considering a spellcasting feature (which mostly just grants slots for casting and how/which spells you get access to cast).

Quote from Kronzypantz >>

 

and most expanding features like this do note a class requirement in leveling, because multi-classing was accounted for in the basic rules.

 
Actually most don't and the ones that do, typically newer ones, do so for clarification and assistance rather than necessity - because they've since realised people can be odd little ducks and try to exploit every tiny thing they can. They assumed people wouldn't need it be clarified each time but people proved them wrong so they adopted the approach of clarifying more. You'll note that in One D&D there's a lot of different approach to the language leaning more to repetition for ease. 

In other words, later features start spelling it out more out of pity for the readers who didn't get it.

Fighter’s extra attack was written in 2014. Im struggling to find examples of class abilities that are not spelled out that way.

The same situation exist for the Champion feature Superior Critical, its not a Fighter Class feature but a Martial Archetype feature that improve at level 15 in the Fighter Class.

Quote from Kronzypantz >>

Fighter’s extra attack was written in 2014. Im struggling to find examples of class abilities that are not spelled out that way.

You must not be looking very close then.

Just a quick scroll through of the Fighter nets several.

Action Surge

Once you use this feature, you must finish a short or long rest before you can use it again. Starting at 17th level, you can use it twice before a rest, but only once on the same turn.

Indomitable

You can use this feature twice between long rests starting at 13th level and three times between long rests starting at 17th level.

And there are a few sub-class features with similar format.

The Sorcerer also has such wordings.

Metamagic

At 3rd level, you gain the ability to twist your spells to suit your needs. You gain two of the following Metamagic options of your choice. You gain another one at 10th and 17th level.

The Bard has this.

Expertise

At 10th level, choose two more of your skill proficiencies. Your proficiency bonus is doubled for any ability check you make that uses either of the chosen proficiencies.

And Barbarian.

Brutal Critical

This increases to two additional dice at 13th level and three additional dice at 17th level.

If you think that any such feature that doesn't specify class level is activated by your total level regardless of which class those levels come from then you are way off. Cantrips and your Proficiency Bonus have specific wordings to show that they work on total level, almost no other feature does.

Not at all. The improvement is a stand alone subclass feature.