Short answer

Bright, sharp primes, when paired with high-resolution sensors, can be a viable alternative to slower, variable aperture zoom lenses and enable effective zooming. Constant aperture lenses, if you can afford the price and bulk, are the better choice. The exact impact on resolution and light capture will depend on the exact lenses being compared.

Long answer

I did a fair bit of research about this for a camera purchase, and I thought I could share it with the community.

How well cropping compares with the performance of a zoom lens depends on the zoom lens (of course). It is quite obvious that constant aperture zooms will be better than cropping because they maintain the same light quantity even when zoomed-in. But I wondered: how much better are variable aperture lenses for capturing light, compared to cropping?

When we take central crops from a photo, we reduce the angle of view (i.e. we zoom). However, by cropping, we also effectively reduce the amount of light that makes up our image (see equivalence). The light loss that happens with cropping is quite predictable: there is a linear decrease with resolution.

Thus, cropping results in an image that is lower in resolution but otherwise equivalent to a natively zoomed image with a higher F-number. For instance, a reduction in image size of 50% would equate a loss of 1 EV (a halving of the light quantity) and therefore be equivalent to a loss of 1 aperture stop. I verified that by comparing the crops from an image at 35 mm equiv. F2.3 with the calculated equivalent images taken at 50 mm F3.2 and 75 mm F 4.5.

They are very similar, and I share them together with the code and files I used for calculating everything in R here.

Concrete examples

Note that here we assume that we have sharp lenses that are capable of resolving the camera's sensor. Also, zooms can lose some sharpness at the tele end.

Zoom against its own at wide end

Here you can see how the Panasonic LX100 at the wide end compares against its own zoom, and against the Panasonic Leica 10-25mm F1.7: numbers show cropped image resolution, relative to native resolution

Note that the Y scale shows regular increments in aperture value, expressed with the more common, but less intuitive F number. Interestingly, the focal length grows increasingly rapidly with cropping (i.e. with decreasing resolution).

Kit lens against prime

Here is the comparison between a typical APS-C kit lens and a modestly bright and wide prime: numbers show cropped image resolution, relative to native resolution

Super-zoom against bright prime

Here is a comparison between a longer zoom lens and a brighter prime: numbers show cropped image resolution, relative to native resolution

It seems pointless to buy kit zoom lenses, but that is not new. In other words, variable-aperture zooms look only somewhat better than cropping when it comes to light capture, and seemingly only serve to maintain high resolution when zooming.