There are plenty of contracts and escalations that include extra objectives, and if you want to “do everything right” (meaning getting 5 stars), you’ll need to get SA while following all these objectives. It’s not like Freelancer suddenly made the core Hitman gameplay totally different, objectives have been present since H1.
If it made no difference then there would be no point in including them in the first place. They’re here to give the players options and to encourage them to try certain strategies they might not have used otherwise.
If you don’t choose a prestige objective or don’t do it you lose the amount of money it would have provided you, the same way that you lose the amount of money the other 3 provide if you fail or don’t do them. They’re all technically extra bonuses that reward players for doing certain things, instead of penalizing them if they don’t. You only get “penalties” in Freelancer if you get killed, let a leader escape or leave a mission without killing all targets. The first two penalize you by ending the campaign and the third one penalizes you by alerting other levels. Getting less money is not a penalty, it’s a bonus you can fail to get if you don’t do certain specific actions (and in the same way, safes and couriers also are).