No, you don't sacrifice refresh rate! The refresh rate is the same. 50 Hz interlaced and 50 Hz non-interlaced are both ~50 Hz, approx 270 visible scanlines, and the display is refreshed at ~50 Hz in both cases. The difference is that in the 50 Hz interlaced case, alternate frames are offset by 0.5 scanlines, the producing device arranging the timing to make this work on the basis that it's producing even rows on one frame and odd rows on the other. And the offset means the odd rows are displayed slightly lower than the even ones.

This is a valid assumption for 25 Hz double-height TV or film content. It's generally noisy and grainy, typically with no features that occupy less than 1/~270 of the picture vertically for long enough to be noticeable. Combined with persistence of vision, the whole thing just about hangs together.

This sucks for 50 Hz computer output. (For example, Acorn Electron or BBC Micro.) It's perfect every time, and largely the same every time, and so the interlace just introduces a repeated 25 Hz 0.5 scanline jitter. Best turned off, if the hardware can do that. (Even if it didn't annoy you, you'll not be more annoyed if it's eliminated.)

This also sucks for 25 Hz double-height computer output. (For example, Amiga 640x512 row mode.) It's perfect every time, and largely the same every time, and so if there are any features that occupy less than 1/~270 of the picture vertically, those fucking things will stick around repeatedly, and produce an annoying 25 Hz flicker, and it'll be extra annoying because the computer output is perfect and sharp. (And if there are no such features - then this is the 50 Hz case, and you're better off without the interlace.)

I decided to stick to the 50 Hz case, as I know the scanline counts - but my recollection is that going past 50 Hz still sucks. I had a PC years ago that would do 85 Hz interlaced. Still terrible.