My interpretation is that the data trails are so troublesome that you don't even want to bother with them, to the point that they didn't make any provisions in the rules for bothering with them. And honestly, that makes a bit of sense to me; any good shadowrunner will be buying everything they possibly can with credstick exchanges alone, and it's not just because they don't want a trail in case the SIN gets burned, but in case anyone is keeping an eye on the SIN for any purpose of their own. Whether it's just harmless advertisement or them trying to pin down where you sleep at night, you don't want the corps to get ANYTHING on you.
Arguments of "it's what a good Shadowrunner does" don't work when players have free will and the characters are not all assumed to be experienced runners.
But, regardless, you do
still leave a data trail. That is part of what fake SINs are for; the books even mention that they accrue purchase history and the like. When arguing about this kind of stuff, you need to keep in mind that those exist and what they are used for.
If you could buy things without making Availability tests at the risk of having to replace your fake SIN (because it started to attract attention), the rules would mention this.
That would be a huge part of purchasing things after creation, deciding "Do I need this rare thing bad enough to try and buy it legally and attract attention? Or can I see if one of my contacts has the skill to find one on the black market?". It wouldn't be something you had to infer, it would be explicitly mentioned
Is it a good houserule? Oh sure! Flesh it out a bit (to determine the exact changes and when to roll to see if your SIN has burned for each purchase) and it would be a great houserule. But it's definitely not
how the base game works, as there's no way such a thing wouldn't be spelled out if it was intentionally an option. It's just too big of a difference.