The bigger companies, which self insure, can dictate that they will cover somebody from day 1. They don't have to, but they can. They will still require you to signup by a deadline, but will cover any expenses you have starting from day 1. The fact they self insure means that they have a more control over certain rules. They still use an insurance company to arrange doctors, hospitals and to process paperwork, so the card might take weeks to arrive but the coverage starts before the arrives.
Medium sized companies will not have the power to dictate the rules they want on the insurance company. Therefore they don't have the flexibility in this area. They will still give you a deadline to register, but will start coverage for new employees on a set schedule.
In some cases a boutique company could decide to cover an employee starting on day 1. Their size doesn't allow them to dictate to the insurance company the start date, they just cover the employee from corporate funds for that initial period. This is vary rare.
The reason why an insurance company likes a set schedule for the new employees is that is simplifies their processes. They know when they will process the accounts for the new employees, they know that they don't have additions every day of the month. They also don't have to bill for partial months.
In a related situation how companies handle the end of the employment. Some will continue your policy to the end of the month, others will end it on the last day of employment. Knowing before quitting is important to make sure that you don't count on insurance that isn't there or don't take advantage of the insurance that does exist.
I don't see how there are a large number of employees who find a job, get insurance and quit as soon as they get the expensive treatment. Just by chance there will be some, but it can't be a large number.