Conversions take time. Time to gather the parts. Time to build. With a off the peg or used fixed, you can ride immediately.

Conversions take effort and expertise. There's lots of easy stuff, then there's lots of stuff that's not so easy (like chainline management). Look at how many threads have "help" and "converting" or "conversion" in the titles.

New bikes have warranties. New bikes get complimentary services at most shops. With a new bike, you know exactly what you got, not "God, I hope this works."

It seems that most (not all) people convert because they don't have the cash to buy a fixed/track bike. Some people like conversions because it's a learning experience. If you can afford it and your conversion candidate isn't anything super-special (the Del Rey doesn't seem such), I say just buy a complete fixed bike either new or used and start riding immediately.

Just about every major bike manufacturer makes a single speed / fixed bike nowadays. You have LOTS to choose from.