Resolution mystery for QuickTime Player recordings of iOS devices

[Doctor Q]

I'm puzzled about the .mov file resolutions that result when I use QuickTime Player to record various iOS devices while they are connected to a Mac. The Mac has screen resolution of 2560 x 1440, if that matters. My tests show that none of the choices in QuickTime Player's View menu affect the resolution of the recorded iOS device.

The mystery is why iPhones record at their native resolution but an iPad does not.

Device: iPhone 6
Device's screen resolution: 1334 x 750
Resolution of recorded movie: 1334 x 750

√ The resolutions match.​

Device: iPhone X
Device's screen resolution: 2436 x 1125
Resolution of recorded movie: 2436 x 1126

√ The resolutions almost match. I assume that 1125 changes to 1126 because the resolution must be an even number.​

Device: iPhone 11 Pro Max
Device's screen resolution: 2688 x 1242
Resolution of recorded movie: 2688 x 1242

√ The resolutions match.​

Device: iPad (6th generation)
Device's screen resolution: 2048 × 1536
Resolution of recorded movie: 1600 x 1200

Why is it smaller? What can I do to get a higher-resolution recording?​