The quarter round allows a bit more room for the floor to flex, which can be a very good thing. However, see Houzz Photos under "wide baseboard molding" for numerous examples of no quarter-round. In addition, there are flatter profile trim pieces available.

I also have 5 1/4 baseboards. I opted for no quarter round. Think it looks better without.

I think it is a lot cleaner look without. The quarter round is used to hide the imperfections between the floor and base. I have scribed the base to the floor so quarter round would not have to be used however this is labor intensive, If the installer takes his time to install the base and there are no bad spots in the floor it will turn out fine.

Yes - most floor installers will not scribe the baseboard to the floor as Jeff H does. Many might not even know how as they just install floors. If you are unusually lucky, your floors will be perfectly level and the baseboards will be installed perfectly level sitting perfectly on the floor with no gaps. Unfortunately, the nature of houses is they are rarely perfectly level or plum. if the gaps (both up and down and across) between baseboards and floor are noticeable, then you will need the quarter round.