I don't fully agree with the OP, and I do think the term has its uses, even if it's seriously overused, just like any other design term on here, like "counterplay" or "overloaded". In terms of balancing, it's true that no effect is free, because it's factored in as part of a champion's power budget and they're balanced around it, so removing Garen's armor shred or Yasuo's shield would obviously constitute massive nerfs and drive both their win rates down. It is also true that there are very few effects that are truly "free" in a champion's kit, as they all tend to be conditional. They still exist, like Shyvana's 10% bonus damage to dragons, or pretty much any base stat (all base stats are permanent, non-conditional power), but as a general rule, players do have to expend some effort to gain access to their power.
However, this doesn't mean that every mechanic requires a fair amount of effort for the power it provides, and I think that's the core of what the term "free" gets to. Pressing a button to get tons of general-purpose power on-demand with little cost or downtime, for example, tends to not be great design, as is the case for Mundo's E or ult, or Kayle's E at high CDR. Acquiring or applying tons of power for a conditional that isn't particularly difficult to satisfy also tends to feel unfair, as is the case for, say, Yasuo's armor pen on ult, or pretty much any Juggernaut's kit against another melee opponent. It also doesn't feel great to play against a champion innately capable of countering a core intended weakness at little real cost: Jhin, for example, is supposed to be one of the most immobile ADCs in the game, due to how much range and CC he has elsewhere, but also has pretty regular access to a speed boost; Ekko is meant to be a squishy assassin, but also has a shield and a self-heal that can make him pretty naturally tanky; Camille is meant to be a Diver, i.e. a champion with great back line access and poor escapes, yet can use her E to jump to a wall 800 units away, and then jump over the wall from there, effectively giving her a ~1200 range escape that can be brought to a 6-second cooldown (Lee Sin has a similar problem with his ward hop).
While players in general often tend to be fuzzy on balance and design for some champions, we now have clearer standards for strength and weakness profiles offered by Riot themselves, particularly when they release dev blogs for particular champions detailing their development process, and as such we tend to be much more sensitive to the kind of features a champion is supposed to not have. Therefore, when a champion gets access to something that they're not supposed to be good at, or that mitigates or eliminates one of their core weaknesses, that kind of power tends to be perceived as "free", because it feels like that champion is receiving something that they just don't deserve. At its core, "free power" is power that feels undeserved or unwarranted on a champion's kit, so even if the term itself is overused, and even if all power is factored into balance, there are still situations where it's justified to use it.
