Typing is always important in the game of pokemon but having a balanced mix is not necessary for a strong team in this generation. The 6 pokemon I listed are 3 normals, 1 psychic/grass, 1 ice/water, 1 rock/ground. That's 5 pokemon weak to fighting. Is that a concern? No. Fighting pokemon don't have access to the same strength moves they do in later generations and are weak to the common Eggy/Alakazam or fully walled by Slowbro. Submission is not nearly as scary as Close Combat. Fighting types are such a liability that you can bank on not seeing them. I'm pretty confident my team would handle Machamp just fine with Exeggutor as my only "type" counter.
The real counter to psychic types is Chansey.. that's why it's on every team. It can eat paralysis, paralyze them back and tank repeated special hits only to Softboiled them away.
Hell, the only reason for even using Golem/Rhydon is to make sure you're covered in case the opponent has Zapdos so you can wall it. The Ground/Rock mons aren't going to be saving you against normal types.. all the good ones have at least one SE move to hit them with (Surf/Quake/Blizzard/Bubblebeam). They're useful for strategic switching but they don't counter much based on typing alone.