I think there were a number of real reasons for 'a look', and most of those no longer apply...but others may have taken their place.

The real ones IMHO are historic.

35mm Changed Photography

Leica invented 35mm and suddenly a lot of professional reportage and suchlike became infinitely more portable. This meant that there were Leica type photographs, that had nothing to do with the quality of the image.

35mm Changed Image Quality

'Actual' image quality actually took a nosedive with 35mm, but so long as this was factored...it could be said it was not 'worse' but 'different'.

Grain increased but portability meant reduced use of lights and more pushed ASA/ISOs for motion shots. The result for street or war photography was a texture. Meanwhile where film speed was not so critical, 35mm was still sufficient to capture fairly grain-free images. We should remember analogue crystal grain can be attractive in a way that digital noise never shall.

Silver Nitrate

At the time Leica was making its name in the '40s and '50s as the only 35mm pro system, I understand monochrome media used far higher concentrations of silver nitrate than later film. Images from that time (the actual prints, not scans on a monitor) have a luminance and quality that I think was lost in later film. As such, by the time all the other pro 35mm systems came out they could not match the old Leica images ..the 'Leica look'...but here's the crunch...nor now could Leica!

Non-Coated Lenses

The Olympus OM-1 was perhaps the next game changer, it was actively designed to knock Leica off its pedestal and largely succeeded in professional circles. It actually fits the Leica case, up to but of course not including, the pentaprism and was originally called the M1 until Leica objected. It too had uncoated lenses and again IMHO matches the 'Leica look' allowing for the fact the silver nitrate was now reduced for all.

So what then is the latter day 35mm Leica look? A high-performing professional uncoated lens, but I disagree that this has to be particularly sharp. What it has to do is have a very good bokeh, good contrast, and a fast aperture.

Prime Lenses

Most Leica owners seem to stick to a prime. In contrast, most SLR owners these days tend to use a zoom. Zooms are slower than primes, so you lose the narrow depth of field the prime offers and they generally render less well.

Also the zoom means many fail to really get up close to their subject...so this can make the image appear flatter and relatively lifeless. IMHO it was a sad day Olympus added zooms to their OM system.

Uncoated Lenses

Uncoated lenses were superior for monochrome but had issues for colour. Leica tends to go with monochrome a lot.

I tend to use uncoated lenses on my DSLR when shooting monochrome and even on digital I think it does make a difference, but like the notion that a modern Leica has an inherent look, I might be kidding myself! It definitely makes a vast difference shooting infrared. Most modern lenses, irrespective of quality, are plagued with issues on an infrared DSLR.

TODAY

I think a modern photograph on a Leica has no more of a special look than any other professional camera with a professional prime in the same kind of price band. Any suggestion that it is superior is almost certainly just that many compare the images with those taken on comparatively budget kit and usually shot with a zoom. Likewise anyone investing in a Leica would have to be pretty serious about their photography and probably fairly experienced...so the typical Leica shot is not really comparable with the typical shot of a consumer camera.

A FORMAT COMPARISON

Today we see micro four thirds creating pro solutions on tiny sensors with many pros rejecting the pro claim because of this. Noise increases, resolution diminishes, "negative" size is limited at around 16mpx and one needs twice as fast lenses to get compsrably shallow depth of field, just as was the case moving from medium or large format to 35mm, if we can claim that was ever achieved.

As such, within MFT, "Acme Camera Co." charged the Earth but made only top notch super fast lenses and made super compact portable bodies by exploiting the small formar..they'd be a Leica scenario for today. Pretty soon people would talk of an "Acme look".

Personally I find the Leica M series actually feel bulky, even " vlunky" today. I used an M2 for a while and have to say it never came close to the joy of the Olympus fitted with an f/1.2 lens, though the rangefinder was incredibly bright ( unlike on a series lll or its Russian clones, and worked a treat.