I don't like saddles that sag or hammock. I like them to be basically flat and stay flat, so that I can easily shift myself fore/aft to relieve pressure point as I ride.

Tensioned leather saddles are very much prone to sagging under normal use. Look at any well-used Brooks saddle, it'll probably look a bit like a Pringles potato chip. Some Brooks will sag all the way to the rails if the user doesn't discard it soon enough. The tension bolt in a Brooks saddle is limited in it's capacity to compensate for the gradual-but-certain elongation of the leather saddle.

To be fair, many bicyclists love the sag/hammock feel of a broken-in Brooks saddle.

A selling point of Brooks saddles is the great width of the saddle. However, you don't need more width for comfort, and often the cause of discomfort on a narrower saddle is not the saddle width.

OP, if you have a $10 saddle that suits you, then you should get a few spare saddles and count yourself very lucky. Don't fix it if it ain't broke.