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The phrase "a prohibitively high" is correct and usable in written English.
It is typically used to describe a cost, price, or barrier that is excessively high, making it difficult or impossible to proceed with a particular action or decision.
Example: "The cost of the new software was prohibitively high for our small business, so we decided to look for more affordable alternatives."
Alternatives: "excessively high" or "unreasonably high".
Exact(22)
Globality, however, often has a prohibitively high numerical cost for real problems.
Over the last decade, companies have developed novel ways to overcome these hurdles, but at a prohibitively high cost.
That project was also hampered by the owners of the Mets, who demanded a prohibitively high rent for use of parking lots at Citi Field.
However, the sapphire waveguide has a prohibitively high RI (1.7708 at 546 nm) for unmodified monitoring of the RI changes of aqueous solutions.
Maintenance much higher than $1.50 per square foot in a full-service building can also dull a buyer's appetite, as can a prohibitively high flip tax that handicaps a seller's willingness or ability to negotiate.
Seeking to fend off the proposed storage facility, the Nevada legislature earlier this year created a new county, called Bullfrog, with what they hoped was a prohibitively high tax rate.
Similar(38)
We at Rocky Mountain Institute built our net zero headquarters, the Innovation Center, in Basalt, Colorado to show that a high-performance building could be achieved in the coldest climate zone in the U.S. Despite these and other success stories, a common perception remains that achieving net zero energy, is too expensive or comes at a prohibitively higher cost than conventional construction.
For example, you wouldn't see Corbyn wind up opposing supporters by attempting to change party rules retrospectively; or making the price of a democratic "say" prohibitively high; or taking away the rights of local democratic bodies to express themselves.
In the 1990s there had been a dramatic increase in the adoption by firms of so-called "poison pills" that could take effect in the event of a hostile bid, such as the ability of the firm to issue vast amounts of shares to friendly investors, thereby greatly reducing the value of shares already bought by the bidder and making the price of buying a controlling stake prohibitively high.
Apartments are typically low risk — everyone needs somewhere to live, and in many cities, the cost of owning a home is prohibitively high.
In contrast, solutions offered by brick-and-mortar outsourcers are effectively custom-built each time, making the marginal cost of an additional customer prohibitively high.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com