The spreadsheets you're seeing with a lot of tests on them are likely for cats who are on the Tight Regulation protocol. With that, we keep the cats in the normal range of numbers for as much of the day as possible using one of the depot insulins. More testing is needed both to make sure the cat doesn't drop into hypo territory because they're running only maybe 30-40 points above that most of the time and also because with the depot insulins, dosing adjustments are made based on how low the dose takes the cat not on the pre-shot number. As the nadir, or low point, can change from cycle to cycle, capturing that lowest point also requires more testing.
I don't think you're going to find many people on here who would agree with your vet's opinion that testing once a week is sufficient as, no matter what insulin you use, each cycle will vary. Insulin is a hormone so the injections we give aren't like giving an antibiotic or a pain medication where the effect remains the same day after day - with hormone treatment like insulin, a cat will vary in how it uses the insulin every time. The reason that we recommend getting mid-cycle tests is to find out how low the dose is taking a cat - the pre-shot number may be quite high, but that doesn't guarantee that a cat can't drop into hypo territory around nadir which as you know is dangerous. I have personally seen drops of 300+ points in 6 hours (and I know other people have had their cats drop even bigger amounts in a shorter time) meaning that a number that looks perfectly safe (in fact higher than is ideal) can turn into a potential hypo very quickly if not monitored.
While your vet does have a valid point in saying that many cats can cope with being less regulated than dogs, that does depend on the cat and on your ultimate goals for your cat. If remission is something you would like to achieve, then regulating loosely is very unlikely to allow that to happen. On the other hand, if you are happy for Tigger to be on insulin long term and aren't too concerned about trying to get him OTJ then keeping him above normal range but below the renal threshold may be sufficient for you. That's a choice that no-one else can, or should even try to, make for you.