Well Bob let me help you out here with finding some adequate long range .338 bullets.

225 gr TTSX SD .281 BC .514 MV out of my 24" gun 2880 FPS

https://www.barnesbullets.com/bullets/ttsx/
250 gr LRX SD.313 BC .602 I haven't shot them out of my rifle so I don't know the velocity but the book shows about 2700 ish

https://www.barnesbullets.com/bullets/lrx/
225 gr Nosler Accubond SD 281 BC .550

https://load-data.nosler.com/load-data/338-winchester-magnum/
250 gr Nosler Accubond BC .575

260 gr Nosler Accubond BC .778

225 gr Hornandy Interbond BC .515

https://www.hornady.com/bullets/rifle/#!/
250 gr Sierra Boat Tail BC .565

https://www.sierrabullets.com/wp-content/uploads/2019/10/BC-chart-rifle.pdf
225 gr Cutting Edge MTH BC? doesn't say but from the looks of it they are well above .500

225 gr Lazer Tipped Hollow points BC I'm guessing .600 ish

https://cuttingedgebullets.com/338-225gr-lazer-tipped-hollow-point
I'm going to stop there because this is more than an adequate choice of long range elk capable hunting bullets for the .338 Win Mag your choice increase exponentially if you want to move up to a bigger cased .338. And when it comes to strictly working better the only place a 7MM beats it is in recoil. For an overall well rounded elk rifle I'll take a .338 everyday. Strictly speaking of course you are 100% wrong in your statement about a limited choice for high BC elk bullets for the .338.