In F1 it is one of the top honours, so much so the defending champion has to run #1 by regulation. But the other numbers are largely irrelevant in F1, where you identify cars by livery and helmet design.
It used to be that everyone kept the same number, except the new champion would exchange #1 (and his teammate #2) with the former champion (and his teammate). Hence why Ferrari and McLaren continually swapped the #1/#2 with the famous #27/#28 for so many years. That ended in the 90s and now the champion and his teammate take #1 and #2, the rest of the order decided by Constructors’ Championship positions, so nobody can build a long-term brand around a number (think Nigel Mansell Red 5). Pros and cons to that. I think I’d prefer it if they set the rest of the numbers like IndyCar or MotoGP.
Of course the one thing F1 teams do wrong is run with tiny car numbers because if they were any bigger they’d take up valuable sponsorship space. I like that IndyCar has giant numbers usually on the rear wing endplates. Sponsors must know those are valuable.

In MotoGP it is like IndyCar. Everyone runs their own personal number and the champion can elect or refuse to run the #1 next year. Rossi never took up the option, and his famous yellow 46 may not have passed into legend had he done so since he’d have run #1 year after year (back in his successful days), but he is very much an exception.

The only thing I disagree with is calling Morgan Shepherd forgettable. He was a solid second-tier driver in the Kyle Petty/Sterling Marlin/Ken Schrader/Bobby Hamilton vein and overachieved in lots of cars, even improving on what Dale Jarrett did in the #21 (by quite a bit, actually), and finishing 5th in the points in 1990 in the #15 when Geoff Bodine was like ten positions worse in ’92-’93. Rick Mast, even though I liked him, I’ll agree. Steve Park was by far and away the best of the NASCAR #1 drivers in recent years, or would have been had he not been hurt at exactly the wrong time as he was beginning to break out.

F1 has had years when they did not change numbers at all. There have also been years where the champion retires and his replacement runs #0 and the teammate #2.

If you look at F1, the fans are motivated by team and nationality. The Germans like the German drivers, the Brazilians like the Brazilian drivers, etc, etc. The same goes with the teams. If your a Ferrari fan you root for whoever is driving for them at the time. You don’t stop rooting for them if another driver takes the seat. The same goes with McLaren or Red Bull or Williams. The individual driver is less important then his nationality or the team he drives for. The positive to this and IMO the reason F1 has always maintained the largest fan base in the world is that when a driver leaves a specific team their is no discernible drop in the fan base. So, when Schumi retired the first time, the fans didn’t stop rooting for Ferrari, they moved their affection to Kimi, and after Kimi to Alonso. The important factor is results. The positive to this is that drivers only keep their seats if they are getting results. This is why you see new drivers almost every year on the grid, and by doing that it keeps the sport fresh.

Now lets look at NASCAR where the individual driver is the most important element to the fan base. Over the last ten years, the field in NASCAR with a few exceptions has become very stale. With most of the top drivers pushing closer to 40 or 50 like Martin, the fans are starting to get turned off by the lack of new blood on the grid. The teams are held hostage to the sponcers who have built their ad campaigns around individual drivers instead of teams. So, if a driver like Dale Jr doesn’t get the job done (like Massa at Ferrari) would he lose his job? Not a chance. Dale was horrible for three years with Hendricks, but because he is popular the thought of replacing him never crossed their minds. In those same three years a driver like David Reutimann won two races for a midpack team and he loses his ride because the sponcer wanted a different driver for their campaign. Heck, Danica is going to get a full time ride next year, not because of ability, but she sells product. How many more years will the same fifteen guys dominate NASCAR before the fans become turned off?

When teams assign numbers to a driver, it makes it easy for the fans to follow a specific driver on the track. It also allows them to market that association of the number to the driver. Gordon is 24, Jimmie is 48, Senior was 3, etc, etc. This is good for the driver, but what happens when the driver retires? Do they lose all those fans that they have built around that specific driver? If Junior retires next year, would NASCAR lose a large chunk of fans? Of course they would and that’s why you will see the same drivers for another ten years until they need help getting in the car. When Micheal retires at the end of the year in F1 will fans stop watching. No, because the team and the drivers nationality trump any individual fan base.

IndyCar is more like F1 with the diversity of nationality and that’s a good thing. The fans who follow American drivers have guys they can root for, the Brazils have their guys, etc, etc. This helps expand the fan base into other countries such as Brazil and England (who had better ratings then in the USA). By using the F1 number system it will also help promote teams that fans can get behind. Teams like Penske, Ganassi, Andretti, etc. Those teams aren’t going anywhere, but the driver might be.

The AMA also used to shuffle the numbers every year based on the previous season’s point standings. I never cared for this with dirtbikes or Indycars, because there is something to be said for building a brand around or simply liking a certain number.

The #1, however, is something drivers should be proud to earn. I don’t think they should be forced to run it, but they should appreciate its importance to the point where not running it becomes a very uncommon thing.