Date and Time dimensions serve very different purposes. You must remember that the purpose of a dimension is to describe the event(Fact) that occurred. Whereas a date dimension can be used to answer questions like events on a holiday or events per quarter, the Time dimension usually breaks the grain down to the second (but can go lower) to assign additional meaning beyond just the ticks of the clock.
For example your business may designate business hours as 9am-5pm. You can associate a flag attribute "Business Hours" to each second to allow you to easily identify facts occurring after business hours. If you have multiple overlapping work shifts, you can create a column for each shift to indicate if that time corresponds to that shift.
A time dimension relationship should tell you more than just when the event occurred by adding additional analytical layers to the When.
For example, relating events to multiple time dimensions (e.g. local vs UTC) can also allow interesting analysis across time zones (How much arson occurs between 1 - 2am) or (How much arson occurred after the flying spaghetti monster attacked at 1:23am UTC).
FYI: I would expressly recommend against combining time and date into a single DateTime dimension. Clock seconds are finite (86400 per day); days are infinite. DateTime dimension at the second grain can become unmanageably large very quickly. However, some analysis needs this grain, specifically when looking at events dependent on sunrise/sunset or other attributes that vary based on the Date AND Time.