They could have got the Long Rifle to feed if they had wanted to. They proved that with the Model 63, which has a LOT of parts in common with the 1903.
The real concern at that time was the prevalence of black-powder and semi-smokless loads on the market for the .22RF. The 1903 was viewed as a piece of precision equipment and they didn't want people hauling it apart completely every time it needed to be cleaned.... which would have been every time it was shot. So they invented a new cartridge, which was copied by Remington and called the .22 Remington Automatic and which was NEVER made as a blackpowder or semi-smokless round; it was straight smokeless right from the word "GO!".
As mooncoon has pointed out, the .22 Long Rifle will split, each and every time, in the .22WRA chamber. But the .22 Long Rifle is also LONGER than the .22WRA, even though power is just about the same. All they really did was put a .22 Long Rifle load into a slightly shorter, fatter casing.
One factor that kept sales of the rifles down was the relative scarcity of the special ammunition for the things. Some shops wouldn't carry the special ammo, or else just got in a couple of boxes when they had a special order for the stuff. That left regular .22RF Long Rifle in a wild variety of loadings as the standard: smokeless, semi-smokless, duplex and Black all were available for many years. Gradually, the Black lost favour, followed by the duplex loads, then the semi-smokeless faded, leaving the smokeless as the one-and-only type available. But this took a LONG time, and semi-smokeless still was available for years after the smokeless had become the 'standard' round..... and the 1903 was out of production, replaced by the Model 63, which continued in production until the 1960s.
The 1903, and the follow-up Model 63, both were expensive little rifles to make. Remember, in 1903 you still could buy a brand-new single-shot for under $2.... from Winchester, too! The 1903 and the 63 both were expensive to make and they were expensive to buy. I started shooting a little before the Model 63 finally calfed and I can say honestly that I NEVER saw a single one out in the field. Nobody around here could afford one.... except for the one guy who never shot his..... that the hardware store kept a single box of shells on hand for. He re-ordered about once a year.... a single box.
The ammunition also was expensive even while it was being made, roughly double the price of regular .22 Long Rifle. The ammo price helped to keep rifle production low and the rifle price helped to keep ammo production low.... and the result was rifles and ammo BOTH expensive. But it was a very good rifle and it used a very good cartridge. I still have a box of real old stuff around here, somewhere.
BTW, there also was a .22 Winchester Rim Fire (.22WRF) available, which was a sort-of-a Nineteenth Century version of a .22 Magnum. It was slightly fatter than a regular .22RF and quite a bit longer, always used a copper case and was rather costly. It was for the Winchester 1890 pump rifle, which became the Model 1906 when it, too, became a regular .22RF type. The .22WRF had a lot more wallop than a regular .22RF (and also was copied by Remington, called the .22 Remington Special), but it cost almost as much as the ammo for my Cooey Canuck, which eats .25 Stevens Rimfire ammo...... and GAWD!, but how I WISH somebody would put that number (the .25 Stevens) back into production!!!!
There are over 100 varieties of .22RF Long Rifle available on the market today, all competing against each other for what market there is. You'd think that SOMEBODY would realise that there still exist (literally) millions of old guns that need to be fed.... and they use cartridges like the .22WRA, .22RA, .22WRF, .22RS, .25RF, .25 Stevens, .32RF Short, .32RF Long and all the rest. This dearth of amo for the neatest old rifles is one of the BIGGEST p*ss-offs of living in this century!