While this has no chance of changing anything, I decided to make my own revisions to the Type chart for the sake of rebalancing for a little fun. Here is a chart with my revisions with the changes in bold:
An important thing to note is that I value competitive balance first and try to consider the developers' intentions. For that reason, I don't making think making Flying, Bug, or Grass worse by having more Types resist them is a good idea. I also oppose making Dragon of Psychic super-effective against Steel as that goes against the intentions of the developers too much; Steel was meant to help balance Psychic and was the only Type to resist Dragon prior to the Fairy Type.
My primary goal was to buff the Ice Type and nerf Fairy. I also wanted to make defensive nerfs to Water and Steel. I ended up making changes to other types as a sort of cascade effect. As a result, Rock, Poison, and Bug ended up improving while Ghost became worse. Psychic and Electric ended up becoming more involved as a means of preventing more Types from growing too strong.
I'm not entirely happy with the chart, as Grass remains quite terrible while Water acquired a buff. I also wish I could have done something for Dark and Dragon, but I probably destabilized some stuff enough already. It would be fun to try to make a Gen I ROM hack with revised Type matchups as well as Move and pokémon Typings to make it more balanced, but that would require me not being too stupid to code. Anyway, I am open to suggestions for improvements on this ultimately pointless project (as many developers don't take kindly to fan input and would issue a cease & desist over this.)