This isn't a question of what "ought" to be and cannot be answered for all situations. The issue is not who physically receives the compensation, because that is almost always the pax, not the payor (most usually the employer), but who is to receive it ultimately.

Some forms of compensation such as a hotel room or meal vouchers, are a net zero to the employer which would have had to pay for its employee's additional expenses. But, the bigger issue is what happens to IDB / VDB compensation when it delays the employee and there may be additional direct or indirect costs to the employer.

This is a matter of employer's policy. Most leave it alone, figuring that it's neither frequent not very fair given that it's generally an annoyance and inconvenience suffered by the employee. But, the answer would all depend on what the policy is, if there is one.

The bigger question is whether cash compensation as in an IDB is taxable income. Now that it maxes out at $1,300, this is not chump change and for a person who is IDB a couple of times in a year, this can amount to a serious cash deposit.