I remember being hit by a car on my bike (a famously under-reported incident), but both myself and my girlfriend physically/emotionally were in rough shape all day. We forgot to report it, then it ended up slipping out of our minds.
This is a challenging problem to solve with technology, similar to getting patients to take their daily medication on time.
AFAIK you can file a police report at any time. Whether your report leads to any results is probably negatively correlated with how long you wait to file it, but you can't be sure it won't until you actually report it.
However, many crimes (especially more minor ones) have a statute of limitations, where the crime can't be prosecuted after a certain amount of time.
And older investigations are harder -- a witness in a house adjacent to the crime scene may have remembered hearing a crunch followed by a car speeding away at the time of the accident if interviewed the following day or week, but may have utterly forgotten, or moved away and be impossible to locate, or have become unable to testify due to developing mental incapacity or becoming deceased, if the day in question was months, years, or decades ago. Likewise, the next day there might be tire marks, bike parts, or other physical evidence at the crime scene, but after months or years it will have deteriorated or totally disappeared.
Also police surely know that older investigations are harder, so in addition to the problems with the evidence itself, having an older case you might not be assigned as many police resources because they know there's a lower probability of success, and it's their duty to taxpayers to use their limited number of detectives, etc. on the cases they have the best likelihood of solving, so those taxpayer dollars are used most efficiently.
But this doesn't mean you shouldn't report it. You don't know exactly how your crime will be classified (assault? traffic offense? attempted homicide?), so you don't know what the statute of limitations actually is.
It might be that your report provides the missing piece of a puzzle -- there might be a cold case file in the police station saying, "A local mechanic noticed a car brought in for repairs had bike parts embedded in the grille and blood on the tires, the license and owner information was entered in the case file, and we're pretty sure we know who was driving. But no hit-and-runs had been reported recently, we know a jury won't convict without an identifiable victim, and the investigation was closed due to reaching a dead end."