We tried a similar system with our DD (although lesser amounts) around a similar age. The problem was, the reward/consequence was too abstract. The money is completely imaginary until they get it, and the time between when they leave the towel on the floor and feel the sting of the missing $$ is too long to really make the connection. We found that even when she got not pocket money at all, it didn't really make any change.

So we've separated chores and pocket money. She gets pocket money now but it is not tied to doing chores, and she's expected to supply her own toiletries etc, as well as funding her own (limited) social life. So she's learning about how to make her money last for what she needs. Re the chores, we thought up some more immediate consequences. Removal of devices is one that works very well here. They can be confiscated at short notice, and if the behaviour does not improve, further devices are removed. She's got down to none and having to do her homework in the library at lunchtime (without her laptop) and I can tell you there was a very sudden and steep improvement in her chore-doing around that time!!

Another thing that works (and I have done this) is to make them "practice" the chore (like, on a Saturday morning). For example, you could send him into the bathroom to practice hanging up the towels for 5 minutes. As if they clearly have some difficulty with it so they need to practice in their spare time until it gets easier . Ok so I wouldn't overuse this one but it does make a point. Alternatively, you could have him write down a list of all the chores you do in a day on one side of a piece of paper, to compare with his own (very short) list.

FWIW I think $60 is far too much pocket money for someone who already has an over-inflated sense of entitlement. Pocket money is something you get when you demonstrate that you are a responsible person IMO, it's not an automatic right. I would be cutting that right back (bearing in mind what his actual need-based expenses are), with a view to reviewing amounts when the general level of helpfulness/responsibility improves.