the PITA aspect is more on the straining issue of the tub stopper - strainers need to be: 1) put in place, 2) cleaned out (ours is about once for every 3 minutes of showering), and 3) exchanged reliably for stopper when used for a bath.
It'd be much nicer if there existed a stopper/strainer combo that, true, needed to be removed to be cleaned but was a single unit.
I think I can't have what I want. But the enthusiasm for the stopper/strainer combo from you guys indicates to me that it is not as huge a user turn off as I'd thought. It's not what I'm used to, so I was worried that it would be a blemish in my otherwise almost-perfectly repaired bathroom 
I grew up with the lever kind that looked like a flat strainer, and flipping the lever stoppered it with an invisible mechanism in the pipes. Strainer and stopper in one. But it requires a trip plate to be installed in the piping, something I'm not willing to do or pay to be done.
Another possibility is, and I haven't looked to see if this is the case in my house, a cartridge/pot filter may already be installed in the piping. This was common in older houses. To empty it you go in through the access panel and take it apart. My access panel is inside our closet, which I just installed lovely organizational infrastructure in. The panel is accessible, but it's cantankerous enough that emptying the filter on the required monthly basis is an unreasonable thing to expect to happen - if it exists at all (I suspect it does because of some of the strange clog behavior it's exhibited). So theoretically the "strainer" exists and I'd only need the "stopper", if this is the case. In that case, the lift/turn or standard stopper seem to be equally usable.
But HD didn't have plain old drain baskets available in the store, only the lift/turn and tip toe baskets with coverplates (to replace the levered plate). So I'll check Lowes and my local hardware stores this weekend.
Yinz guys are awesome, thank you
