I agree with everything dd said, except I don't see why Generals shouldn't be allowed to pick Master-cum-soldiers of their own element, because the reason dd gave makes no difference which way round it is. If the Master was the general, they'd simply 'agree' to go for the vet they would have chosen, it doesn't stop other teams trying to get them too, i don't see how any advantage is gained by this
Master is General, gets player in auction - the player was able to be pursued by the other teams.
Master appoints General, that player gets the Master - the player is guaranteed on the team.
Both ways do require the other player actually be obtained successfully in auction, so the agreement can be made both ways, but it's stronger in the latter, since it is two-way - both sides would be making a sacrifice, as opposed to just the Master-General in the former, and so both sides have an incentive to keep the agreement. And Generals will often spend less to get someone outside their element.
Furthermore, for better or for worse, General is seen as the most important responsibility of a Master. Until this is not the case, declining that responsibility should have a drawback.
That being said, this isn't a huge deal to me, like hydras being transparent is. Just explaining my preferences since my reasoning was not clear - 6am post game weak