An NTSC video signal is 6MHz wide. A VCR records it on the tape in the cassette with maybe one 60Hz field per diagonal pass of the head across the tape, with reasonably good analog fidelity. A VHS tape uses a different modulation scheme, with about 3MHz of video (luminance) bandwidth and another 400kHz of chroma bandwidth. S-VHS has 5.4MHz
The tricky part of making a decent (20MHz) oscilloscope out of garbage is high-speed signal detection: either direct analog display or analog-to-digital conversion. Perhaps recording the signal on a video tape, perhaps with sped-up heads, would enable you to do the conversion over a longer period of time using a slower converter, converting different samples on each pass, with the tape paused.
A NTSC VHS VCR head rotates at 1800 rpm, each rotation covering a 60Hz field, lasting 16.7 milliseconds. If you were to rotate it four times as fast, 7200 rpm, each such track would only last 4.2 milliseconds, but could plausibly have up to 12MHz bandwidth, or 21.6MHz for S-VHS.
4.2 milliseconds is a ridiculously long recording time; at 60 megasamples per second, it’s 250,000 samples, hundreds of times longer than is necessary for a storage oscilloscope. So, if it were mechanically practical to speed the heads up further, it would be a good idea.
(See also files TV oscilloscope, Laser printer oscilloscope, and CCD oscilloscope.)