A format of this nature already exists in Japan for the Base-Neo format. It’s called the Hall of Fame format, and uses an eight point deck building system to restrict the cards you named and many others, creating a nostalgic format with a broad card pool that enables decks built around cards from across first and second generation (excluding e-card). For example, Super Energy Removal is worth 5 points, Energy Removal and Computer Search are each worth 2 points, and Blastoise is also worth 2 points, so if your Rain Dance deck runs two Blastoise, you won’t be able to abuse Super Energy Removal. The Hall of Fame lists are moderated by the Japanese player base and are updated on a yearly basis.
A classical format that’s currently popular on TCGONE is Prop 15/3, a Base-Gym format where you’re limited to 15 trainers and up to 3 copies of each card (Pokémon, Trainer, and Special Energy alike). It was an actual format that existed… for one tournament… under Wizards of the Coast. There’s no pre-programmed “Prop 15/3” option for Quickplay, but at least fifteen players play this format using Base-Gym Quickplay. It’s not perfect, but it’s more consistent than you’d expect it to be, and the matchups are close.