Winning this game against the best players requires you to maximize your effectiveness at all points of the game. Potions are very effective for this early game. Good players will solidify their advantage very early game, often by level 5. If you really think that you have gained an advantage by forcing someone to burn a potion while you back to the fountain, you are a fool. Consider this:
In the minute it takes you to run to the fountain, heal, and come back, I will keep or cap the flag, gain a good xp advantage, and earn gold by killing creeps. Depending on who I am, I may knock your tower down in that time. If I get up in level early game, your extra banded armor doesnt compensate. All that really matters early game is experience, war score, and space (as defined by how many towers are left and thus how far I can chase you). The way to obtain these things is to win encounters, 1 at a time, usually over flags, and to stay on the front lines. In many cases (but not all), potions do this for you better than armor. I would rather be 2 levels up and 1000 gold short by mid game because thats an easy victory for me.
As some have mentioned, low cost armors are usually the best deal, and, in the long term, can be calculated to be more hp/cost effective than potions. I agree with you, low cost items are the best bang for your buck. When buying persistent items, you should fill your inventory with low cost items first, and slowly replace them with more expensive items to fit your needs. However, when doing your cost/reward calculations, you have to consider the battle winning effect you get with potions. With potions, assuming you are using them properly, you are not just purchasing XX health/$ or XX mana/$, if they work, you are purchasing time, experience, and war score.
Potions dont work for everyone, and I am not advocating them under all circumstances. I always look to see which enemy DG's I am fighting before I make initial purchases and choose the items that fit them. For example, enemy UBs and I am any assassin? - Probably BOF, Banded, 2xMana Pots, with generals it would be similar but I would buy/summon/sell monks. Am I fighting burst damage on the other team (e.g. Oak/TB, Sedna/TB)? I am probably getting health potions.
Potions can certainly provide you a strong early game advantage, and, if you are the type of person who likes to win early/mid game, thats what you want.