A person with flu and fever would probably stay home and just rough it out, a person with fever fearing the coronavirus will probably rush to the hospital.
If everyone having a fever in a flu season would go to the hospital and would demand medical attention we would be running out of hospital beds in normal scenarios as well.
You don't get admitted to hospital because you ask. You get admitted to hospital because a doctor admits you. Currently even covid-19 patients don't get admitted to hospital by asking. They need to be pretty severely ill to get admitted to hospital. Health care professionals are triaging as much as possible, and sending people who are suspected (or even confirmed) to have covid-19 back home unless the patient really needs to be admitted.
Despite all this triage hospitals are over run and many countries are experimenting with field hospitals built in large sporting gym halls or convention centres.
One thing that doctors are telling us is that covid-19 is not like flu for their patients.
They don't want you at the hospital unless it is absolutely necessary. Got a fever and still able te breath: stay at home.
It doesn't really matter whether the odds are more like winning a bottle of wine in a charity raffle or losing a game of Russian roulette.
You don't get a hospital bed just because you ask for it, you get one if a Doctor thinks you need one.
So your premise is inaccurate.