I thought of a few different names for this... Non-Blue Belcher, Land Grant Belcher, Dumb Belcher, Truant Belcher, Drop-Out Belcher, etc. but No Academy Belcher is the best descriptor, to differentiate this archetype from the Blue Belcher variants that tend to operate by tutoring up Academy and generating lots of mana via Academy. Those decks also tend to play counterspells, and these variants do not. Not all of these decks play Land Grant, and they don't all play the same colors, but none of them play Academy or a significant counter suite.
This topic is going to be a bit of an intro, discussion, and some decklists, but not a full primer. I don't have all of the information or expertise to make a full primer. I just want more people to talk about the decks and try them out.
In my mind, the quintessential deck for this is RG Belcher. Finding lists on deck aggregators for this deck is extremely difficult, and I think the reason for this is because I only know of one player who plays this deck: Nat Moes. Here is a list he posted in a 2015 article:
##RG Belcher circa 2015, Nat Moes
Since then he has splashed blue for Tinker and Twister, which I believe to be significant improvements.
The unrestriction of Yawgmoth's Bargain has turned a previously gimmicky deck, Black Belcher, into a potentially real threat. This deck gets to play the superior Dark Ritual card, but plays Tendrils over Empty, and Belcher frequently can't count to 10. Now that we get access to 4 Bargains, a more reliable game plan is to resolve Bargain, draw a bunch of cards, and Belcher the opponent or kill with Tendrils. Here is a sample deck that I have drawn up, but have not tested in a tournament:
##4 Bargain Belcher post unrestriction, test deck, mediumsteve
// 60 Maindeck
// 26 Artifact
// 11 Creature
// 4 Enchantment
// 9 Instant
// 1 Land
// 9 Sorcery
Here I give credit to Nat Moes again, who had a black belcher list from 2010 that he and Matt Hazard updated to include 4 Bargains and then I edited slightly.
Remember when playing these decks to use your mana wisely, bait your opponent's counterspells, be brave, and most importantly, have fun. Happy trails.