Steam does have a record of when players actually got around to download the game and even when and for how long they ran it, so the refund clock should start when people actually tried the game or at least when they downloaded it. That refunds rules don't actually follow logic but instead something else, probably means that such refunds don't actually exist driven by genuine will for good customer experience but, more likely, because in some countries there is legislation for online purchases that forces refund windows linked to purchasing time.

You need to consider that Steam needs to pay the publishers at some point, if they followed that rule that you suggested they would need to sometimes wait years to pay a publisher, which makes it bad for publishers. I believe that 14 days is way too short, and they could easily do 30 days, but at some point they need to send that money to the publisher and at that point refunds are dangerous things. For example, imagine they allowed this and one company released a game which was very cheap with lots of promises, so lots of people buy it, eventually they abandon development so lots of people refund it, and no new sales will come for it, so any refund is a loss for Valve. Also credit cards also have some similar rules and problems, what if the card you bought the game is no longer valid?. This is why Valve needs some rules on time limit to protect themselves from those situations.

All of that being said, the time should be longer, and if it's an active game that will give them more sells in the future that they can take the money from they should (and usually do) allow refunds over that time limit. It's strange that yours was denied, I've refunded games over a month after purchasing for similar reasons, they did let me know of the policy but proceeded with the refund regardless.