There are two main differences between hate cards for EHG and hate cards for other mechanics. Firstly, hate cards for EHG need to be deployed before the Golem comes down. When it comes down on turn 2, that's not a lot of time to deploy your effect. With traditional hate cards, you have more flexibility with when you can deploy them (either after they've played their card, or at least later in the game than turn 2). Secondly, many answers to existing problem cards help against other cards as well - silence deals with flying just as well exalted, or entomb, etc. Effects that hate out Golem are basically only useful against Golem decks (Royal Decree nonwithstanding). Imagine the 1 cost spell that reads "Draw a card. Put a 7 cost 3/3 on the bottom of your opponent's deck". It cycles so you can maindeck it, but the hate part does nothing against anything that isn't Golem.

I don't think printing answers is a problem, and in fact lament when they print the questions but not the answers (SITES?!? for several sets) but the answers to EHG either don't do anything against non EHG decks (so we have more pushed cards with narrow thrown own hate like Tocas) or they do horrible things to everybody's hand and deck (Royal Decree). It leaves a very narrow band where cards can be effective and they don't feel good to play with or against.

Finally, hate cards just brings you back to point 2.2 - how do you balance the rest of the game? Is everyone assumed to be playing hate for golem, and you balance around that? Games where you don't draw that hate are going to feel terrible.