Your 'rebuttal' to these arguments I didn't make... it's pretty much made my point for me.

You wouldn't waste a Fireball against a 2/2 creature. So why would you use another spell (Lava Burst) with the same damage potential on it?"

Generally you'll pick pretty much any other option available to you -- including just waiting, or stalling. There are cases where you might want to do it [say, 2/2 damaged Maexxna vs. Ysera, and you have no removal], but generally you'd be wasting an inapproriate card on a situation which has tons of better responses.

Lava burst is a spell with 5 damage potential, whether or not you can choose to not pay its overload. Since you probably will run into a scenario that a 'real' lava burst will be good for in the future [it's not a particularly niche effect], you're going to make pretty much any play that works before opting for lava burst.

"Paying lower cost to kill a weak creature would pay off more if you didn't suffer from overload" Indeed, it'd pay off more on average than it would right now. But overload can be devastating, or it can be absolutely meaningless, or it can be anywhere in between. Which one it is depends on... practically everything.

To deal with overload, You need to have a plan for all the likely 'next turns', and figure out if the mana loss is likely to cause tangible effects, and whether those effects are worth playing the card for. When considering whether you lava burst that maexxna now... Well, maybe you need to let Ysera die, devastating as that may be, because the overload would stop you from Malygos/Coin/Crackle-ing next turn [and then maybe lava bursting the turn after?], and you're at a point where that's a better chance of winning than having a ysera still in play. Or maybe the overload is pretty much meaningless, since you expect to be playing sylvanas next turn and you don't have anything worth putting down with the remaining mana except a totem -- and you're confident enough with that prediction to risk being punished if it's wrong. Or maybe you have sylvanas already and killing a 2/2 with the lava burst lets you guarantee a steal on his... kel'thuzad? Or perhaps it will cause you to have to play your 2-drop over a 4-drop, but maybe it's worth that to stop their mechwarper from... warping. Or maybe you're just lava bursting for lethal and it doesn't matter at all. Every situation is different.

Losing the overload means it pays off a little more to kill a weak creature, on average. But by making the overload only applicable in 'optimal cases' all of that stuff becomes less significant.

Which means you've definitely put much more thought on it then before, even if the situation is tempting.

Nope. If it's tempting to play the card without the overload aspect; it would be worth considering the current card with the overload. Overload can be impactless, and playing the card still wastes the potential of the 'full version'. If it's not worth playing your version, it won't be worth playing the overload version, and you still need to assess the same stuff to come to that conclusion. If it is worth playing your weak version, it well may be worth playing the current version, but you need to think about everything you need to think about when dealing with overload.