I'm afraid but this is a very simplistic view and not how it actually works. You cannot keep your blood sugar stable by eliminating intake of carbohydrate. Something every diabetic who goes into weight lifting learns really quickly (and is well established in literature and known by doctors): protein will increase your blood sugar. It is a very delayed response (3-5h+) and its amplitude is low but it will happen. The process is called gluconeogenesis. Your body has multiple metabolic pathways to create glucose out of nearly any kind of protein found in your body (figuratively speaking) and will do so even in the presence of enough calories (i.e., this is not a response to malnutrition or under-eating).

And then there are all the hormone-based reactions. The classic obvious culprit for raising blood sugar out of nowhere is of course adrenaline but even many others can do so. Stress reactions and others will do this. The glucose in this case comes from your liver which stores it as glucagon. Note that your liver will store glucagon even when you have no carbohydrate intake. As mentioned above, your body will metabolize it eventually.

Your advice about keto is downright harmful. Type 1 diabetics should not go on a keto diet. This is actively advised against and will lead to coma and death. The reason keto works for healthy people is that they actually do not go 0 on carbohydrate and, therefore, still have some amount of insulin in their blood (also for other reasons). Even vegetables contain small amounts of digestible carbohydrates that will trigger trace amounts of insulin and protein, through the pathway illustrated above, will do so as well. Please understand that diabetes is an old and very well researched condition. Modern medicine has a trove of long-term detailed data and statistics telling us what works well and will lead to a side-condition-free life in old age and what will lead to long term damage. This is well understood. Contrary to what you suggested, modern diabetes management does not advise to reduce insulin need as much as possible through dietary means for type 1 diabetics.

Edit: Please note that blood sugar is not a "lower means better" metric. A low blood sugar has risks associated just as high blood sugar has. The "band" of good values is well understood and the headroom "upwards" (i.e., higher than normal values that still won't cause damage) is a lot larger than the headroom "downwards". In fact, standard therapy for diabetics keeps them a little higher than the normal person just for safety reasons. Personally, I stay in a "normal person" range but I also have the luxury of fewer trouble managing my values than others.