I want to put hardwood flooring throughout the downstairs part of my home. I do not want thresholds as a transition from bedroom to closet, bedroom to hallway, from hallway to another bedroom, and from the hallway to an office, and from hallway to recreation room and closets. How practical is this ? Why

No problem, as long as it is not a floating installation. Floaters call for transitions at opening 4 foot and smaller.

LikeFloorguy said,
No problem.
THe installers may want to reverse direction at some of those doorways and use splines.
Your professional installer can explain why you may need to reverse direction if the areas are over 20' in width.

I am installing the hardwood floor myself. What is a Spline?

A spline, or sometimes called a slip tongue, fits into the groove side, making it a tongue side, so you can fasten it down, working in the opposite direction.

You always nail into the tongue side to "blind nail/hidden nail". When you get to an area, that the groove side is facing the way you need to proceed, a spline is glued and inserted, Then a piece of groove side flooring scrap to act like a good board, to hold the spline while you blind nail it close to your scrap.