The rules are in place so that a team can't buy the championship by just running fresh engines every weekend. Could you imagine if McLaren kept putting a new Renault power unit in Alonso's car every race and watched him cruise to victory? The penalties stop teams from just taking the hit in order to collect the wins.
If 'cost cutting' is the goal, perhaps there is another way. Major League Baseball doesn't use cost caps, but a 'luxury tax'. If you want to to pay a player $40 million a year to play, then you have to also give $40 million to a 'poor' team in order to give them a chance to hire decent players too.
So, divide the grid into 'have' and 'have not' teams. Each time a 'have' team uses a new engine part (past the initial allotment), they have to buy the same part for a 'have not' team. The rich teams can run new parts, the 'poor' teams aren't left in the dust.
Obviously this system can be gamed, but shady deals are part of F1 far more than having qualifying be meaningless.