Sure. After ASIs the halfling PC can be as strong as a goliath.
Yes. That's what's nice about floating ASIs, because it allows that one halfling PC to be unusually strong, or it allows that one goliath PC to be unusually weak. Or it allows them both to have whatever Strength they want, but the halfling is particularly charismatic while the goliath is particularly smart.
You're focused on saying that halflings shouldn't be too strong because of goliaths, but what's wrong with having physically weak halflings who are of average Dexterity but are really healthy, smart, wise, or charismatic? Many decades worth of lore has drilled the trope of the "dexterous halfling" into the gaming world's subconscious, so probably most people are going to put at
least a +1 in Dex anyway.
(Which is actually a weird point. Halflings are short and stubby, with short, stubby fingers, but are just as dexterous as the lithe, graceful elves are.)
Am I the only one who has PCs that try to lift or drag heavy things?
No. Why would you think that? But that lifting and dragging things is improved
more by the Powerful Build than by Strength. In one game I'm in, my firbolg warlock carts stuff around. They're basically the party's pack mule at this point, even though there are several other PCs that have higher significantly Strength scores. Why? Because my firbolg has Powerful Build and none of the others do, which makes them better at lifting and dragging heavy things anyone else in the party. Even if I had been allowed by RAW to stick that +1 in any other stat than Strength, my warlock would still be better at lifting and dragging.
Glad you agree. Because this (combined with the fact that Strength and Dex are equal when it comes to attacks) means that the +2 Strength racial ASI is pretty pointless.
And, of course, ASIs aren't just limited to physical abilities, but
mental ones as well, and do we really need to say that one race is smarter or wiser or more charismatic than another?
The bonus issue is due to 5e's overabundance of balance. Balance is good, but too much balance is not.
So basically, as long as the imbalance is in a way that you like, it's OK? Because otherwise that sentence makes no sense.
Edit: I should mention that I've made a
bunch of playtest characters for Level Up, which doesn't have
any racial ASIs at all: they're tied to background, with +1 assigned, +1 floating. I've made both orcs and halflings, and the orcs feel strong and the halflings feel dexterous to me.