I don't think I agree "completely" with your reasoning tbh.
The mk1s never used to wag their tail for a start and certainly didn't rely on the rear giving up "grip". Instead they'd pitch up onto the outer rear, but still have enough front end bite to get you round, but then there was a lot more flex and give in the chassis than a mk3.
I've also driven 306 Rallye/Xsara VTS which is different again. Plenty of front end bite again, but this time the rear feels a little more planted, 'til that rear steer kicks in. The first time it did I thought the back had stepped out but then it sort of catches again and squats and grips.
106 GTI was a totally different beast to the 106 Rallye and of all the FWD cars I've driven it had the most 4-square planted approach. But yet again it never wanted to wash wide.
The only reason your Golf would've is because, and no offence intended here, it's a Golf and I'm sorry but the handling isn't anything like as good as many of the best Frenchies. VAG's tendency has always been for an understeery setup.
None of the above though is any excuse for the swaying rear of the 197s under heavy braking in a straight line.
You're talking many variations, weights and generations pre & post ABS/ESP of a basic formula there though, so you'd expect differences with the amount of weight hanging over the arse and stiffness of chassis, amongst many other things.
French clutter has always been exceptional in terms of handling, sometimes a little on the extreme like a 205, but even its sibling the 309 was a completely different animal despite sharing a common DNA.
No offence on the Golf either, I didn't design the thing so why take it personally! The MKI and MKII were very 'French' in their style, the III and IV were absolute pigs that had a cheek carrying the name. The V with multilink rear is absolutely neutral unless you drive like a spaz.. so steam in and it is hard to swing the arse to correct understeer with a lift, there's too much rear grip. With a few tweaks to 'French' it, it is a very capable car, it's just heavy and needs a quicker rack.
French cars lift off oversteer for fun, they build them that way, and I like them all the more for it hence me buying one. The stiffer the chassis, and I expect the 197/200 is very stiff, it's snappier but should be linear and controllable if you're aware of it... sloppy and a beamed rear kinda bounces as it goes through varying toe, which worries some.
My Golf will do a flat 2 minute lap of Oulton on road tyres, remapped gives similar power:weight of the Clio. I'm willing the Clio on to do even faster and I think it can - so it'll be a good measure between the two for me.
My point was basically either learn to drive with it or alter weight dist & geo to engineer it out of the chassis and make it more planted.
Best guess on his problem - ESP. Back end goes very light, rear tyres lose grip with tarmac, ABS/ESP tries to sort it out and gives a little shimmy as it sends braking force adaptation around all 4 to stabilise the car.
