Yes it will. Why build Battlecruisers or Carriers when they can easily be wiped out by a group of units that is collectively much cheaper? There is no benefit to building an expensive paperweight that doesn’t trade well enough to be worth its cost.
Those players would just mass another unit, like Ghosts, Infestors, Thors, etc.
The only thing you will accomplish by increasing the costs of Battlecruisers and Carriers is removing them from play entirely, since they will serve no purpose.
They couldn’t and they wouldn’t.
A Battlecruiser doesn’t serve a role that is useful for Bio. Most of the units that threaten Bio are ground-based, and Battlecruisers are not particularly well-suited to killing them or soaking damage from them. A Battlecruiser transition from Bio is already very difficult to pull off, and definitely wouldn’t be worth attempting if Battlecruisers were more expensive.
Mech has an easier time fitting Battlecruisers into the composition because of the synergy between long range artillery and a durable buffer, but everything that Battlecruisers do can be replaced by Thors, Vikings, Liberators, or other units. A more expensive Battlecruiser simply won’t have enough value to justify wasting the resources, whether in small numbers or large ones.
Carriers definitely wouldn’t be worth building at a higher cost. Their interceptors do not disrupt the enemy’s target AI anymore (which was the main behavior keeping them useful before), so they actually depend on being worth their cost now. A more expensive Carrier simply won’t be used.
Tempests are the only unit that “may” still see use at a higher cost, but that is only because Tempests fill a niche that no other Protoss unit can fill. They are the only unit that can fight compositions such as Brood Lord + Infestor + Viper + Spore without getting taken over, zoned out of range, or pulled. Even so, if you increase the cost of the Tempest, you cripple the ability for Protoss to handle those cases so they might opt for all-ins to avoid that scenario instead.
No matter what cost (resources, supply, and production-rate) is set for Battlecruisers, Carriers, or Tempests, they have to be worth that cost in order to be useful. If they aren’t worth the cost, then players will never build them.
Increasing the cost just increases the stats that each unit must have, which doesn’t do anything to solve the problems that you are complaining about.