Croyance,
Everybody always seems to have a problem with the various shooting games the way they are. It is the way it is, and like most things, it got that way for a reason.
There is a litany of reasons why centerfire would be an issue.
1.) Space: Many of the countries that participate in Biathlon are crowded, and land is extremely expensive. For most of those countries, building a large outdoor range to permit the shooting of centerfire rifles, with an acceptable safety cone for the 5 to 6 mile range of .30 caliber cartidges would be difficult. Further, it would likely be a facility that would never be used again, because most countries are looking at 100 years or more between Olympics. Most of those countries would have political hell to pay for the razing of the park land or whatever required.
2.)Equipment Races. .22 rifles are affordable, as is match grade ammunition. For a $2000, a competitor can buy a top of the line rifle, and enough match ammo to last for years. The rifle, well taken care of, will easily outlast the competitor. With a requirement to use a caliber of military utility or such, you would add in the whole problem of checking ammunition for power factor, etc. Further, if you put an actual military utility requirement on the cartridge and rifle used, you would be eliminate a large number of the countries that currently compete.
3.) Obsoleting current equipment. You're going to piss everyone off. The competition has been using .22 since the 70's.
4.) Barriers to entry. It's tough to get non-shooters into a sport that requires a punishing tool (for newbies.) Learning how to shoot is tough enough, but having to start with a centerfire, and all the technical detail and recoil that involves would be a high enough barrier that many, many people would not climb it in the first place.
5.) you say the larger cartidges and longer ranges would make the game more challenging. It seems that hitting a 4.5 circle from the standing position at 50m, or a 1.75" circle from the prone position, while winded is hard enough. .22's drift like crazy. It's been stated in more than one place that shooting a .22 at 100 yards is like shooting a .30 at 500
6.) Political feasibility. The IOC is already working to eliminate shooting from The Olympics, even though it is one of the most egalitarian sports. It's politically incorrect in most of the countries that are capable of hosting an Olympics. It's boring as hell to watch, so it won't draw viewers. Many host countries ban any shooting activity that could be construed as martial.
Raising the barriers to start playing the game, both for the athlete's and the host's point of view, and making the activity even more militaristic than it already is, is guaranteed to get Biathalon eliminated from the Olympic Games altogether.