Unpopular opinion perhaps

I think it depends on what feel the time period demands determines whether actives fit in or not.

The main ET games I can think of with active skills are Great Conqueror Shogun, European War 7, and Three Kingdom Conqueror. GCS and Three Kingdoms are very much based on the idea of the fantasy hero, with people like Sanada Yukimura and Lu Bu being larger than life figures who did epic things in battle. It's a little less clear for EW7, but still I think legends like Joan of Arc, King Arthur, and Roland prove enough that medieval Europe had a similar lauding of a general or leader as a superhero.

Now contrast this to the Napoleonic era, WWI, and WWII where the other ET games take place. Here emphasis is less on the leaders and generals and more on their armies and the men who served under them. Thus generals lose their fantastical abilities and become less heroic and more "normal". This is the approach I like about games like EW4 and WC3, generals are killable with normal units, and a problem with WC4's challenge conquest, where the tide of iron consisting of guys like Guderian, Manstein, Leeb, Kluge, etc. seems unstoppable without fighting fire with fire (although maybe I'm just bad, or Germany's steamroll is intentional, which could be the case.)

Essentially, where there's actives, there's a more heroic aspect to those time periods, which is why I like the addition. Besides, it is possible to kill weaker generals in those games, although it's hard to argue that throwing normal units at a fully equipped Yukimura isn't gonna do anything but send good men to their demises.

That's an apt way of putting it, it's easier to lionize things that you aren't living through 

In comparison to EW7 I think the active skills are rather modest, including those of IAP

I don't know, maybe Takeda Shingen has an OP active skill, but even that is not even close to the active skill Genghis Khan has in EW7, for example. Or Richard.

Even stronger generals can be fought reasonably with higher-tier units. Pound with artillery and swarm with sword master - or more reasonably, plant elite samurai to hold the city and just bypass the guy. If you're trying to swarm the guy with ashigaru, I'd argue that Takeda Shingen *should* mow down those peasants.

It's worth noting, apart from the fantasy/legendary element, that we're talking about a time when all soldiers are not created equal, to a much greater extent than once armies are lines of men with shooty sticks and armor goes out of style. Apart from a general's own abilities, he probably commands the best trained and best equipped professional soldiers. For that reason alone, it's not unreasonable for Nobunaga and Shigehide to have actives that basically amount to an extra attack every six turns.

I think that active skills are always problematic in that they allow you to use them all on one turn and one target.
In EW5 this was a necessary tactic to overcome powerful bosses and both regular (aura) and IAP generals (strong aoe skills) gave us means to do it.
But EW7 has gone more in a direction of spamming lots of enemies. To counter this, mostly IAPs have these exclusive skills to kill, disable or counter hordes, while f2p has to work a lot harder to find winning strategies.
In PvP modes (Arena, castle mode and Territory) this becomes overwhelmingly frustrating since daily grinding is supposed to be done quickly and without too much effort.