Taking this specific example:
"...the specific reason T1 diabetics are advised to avoid them is because of how slowly your body breaks down carbohydrates from these foods after consuming."
In my experience most medical professionals lump all potato preparations together as "high-GI foods" and therefore advise that they will raise blood sugar much more quickly than other sources of starchy carbohydrates such as oats, whole-wheat bread, or brown rice. This is backed up by evidence that, for example, baked potatoes can have a GI of higher than 100 (i.e. they raise blood sugar faster than the same number of grams of pure glucose) [1].
Your experience seems to be the opposite, since you claim a "slow" break down. And that's backed by research also! It turns out that the GI of a potato can be drastically changed by cooking method. [2]. Boiling and then cooling a potato causes starches to first gelatinize (raising GI) and then undergo retrogradation, in which hard-to-digest "resistant starch" is reformed (lowering GI again). For those reasons, a cold potato salad (with cooked-and-cooled potato) made with new potatoes (lower GI to begin with due to higher amylose) and mixed with fats (which further reduce GI), might have a shockingly low GI compared to a fresh fluffy baked potato.
All of that to nit-pick the details of your post while agreeing with your overall thesis. This topic is extremely nuanced!
[1] Miller et al. (1992) - American Journal of Clinical Nutrition: Found baked potato to have GI of 121 ± 9
[2] Ek et al. (2012) - Food & Function: Reported GI values ranging from 56 to 94 for different preparations