The 787 is not pressurized from compressor bleed air. Cabin air pressure is controlled by independant cabin air compressors which are electrically driven.

And, I can tell you with certainty that it will cause the engine to take a significant performance hit to bleed air at a higher pressure. First of all, hundreds of thousands of pounds a second is very much on the high side. Second of all, you're just considering total engine flowrate. Most of that is through the fan, which is maybe pushing 1.5 to 1 pressure ratio. At 4psi amospheric pressure at 35k feet, you'd only get 6psi of pressure in your bleed... well below the 14.7 needed to pressurize a cabin to sea level (ram effect might increase this a bit, but not enough to cover what's needed). That's ignoring all the line losses and valve losses. Engine core flow is much less than total flow, and again is much more expensive, especially as you pressurize it more and more. Engine manufacturers are pushed to reduce cooling flow everywhere to improve performance. They are also pushed to use less expensive air to cool lower pressure components. For example, you wouldn't bleed air at the back of the HTC to cool the LPT. GE is moving to composites because they can operate hotter with less cooling. It makes no sense that engine manufacturers would go through all this trouble if compressed air wasn't expensive and they could willy nilly bleed all they want without a performance hit.

There is also the issue that as you pressurize the air, it goes up in temperature. The back of a typical HPC might be at 900F. Too much pressure and you'd make the cabin uncomfortably hot. Now you need a heat exchanger, and even more weight.

Maybe structural issues are more significant than I had originally thought, but engine fuel economy is another STRONG driver here.