I'm not convinced that forcing a European player to provide significant extra weekend availability is the fair way to approach this. The reality is that - inconvenience aside - some European players would struggle to provide 4 hours on the weekend. In the GMT-7 vs GMT+2 example, only the range 1800-2200 on Saturday and Sunday is available for GMT+2 players. This means either being available the entire evening on one of the days, or the best part of both evenings - it is too much to ask of a player to have 50% of their weekend evening made available.
Below shows the mutually acceptable amount of hours over the weekend (where mutually acceptable is defined as between 9am and 10pm local time for both players):
1. GMT+2 vs GMT-7 4 hours per day, 8 hours total on the weekend
2. GMT vs GMT-7 6 hours per day, 12 hours total on the weekend
3. GMT +2 vs GMT-5 6 hours per day, 12 hours total on the weekend
4. GMT vs GMT-5 8 hours per day, 16 hours total on the weekend
I could definitely see a case for asking both players (European & American) to ensure that at least one of their slots (i.e. 2 hours ) falls on a weekend (and that it couldn't straddle the default time - so that it actually presents an alternative option to the American player).
Potentially the amount of hours required could increase as you go down the table above. (to 3 and 4 hours respectively).
I also think that the purpose of the rule is solid. I can't be sure how many American players are actually not joining tournaments because of the issue with International Scheduling, but I can see how having to keep the same time available every single week would get tiresome.
I also imagine that at a certain point (of requiring extra availability) the benefit of better scheduling for the Americans would be outweighed by the effect on their European counterparts.