Journey planner might sort it out, but it wouldn't make the time any less!
If OP's flight lands at (for argument's sake) 12 noon, longhaul flights often run ahead of schedule, so I'd probably want to be there for 12 in case that was the case.
If it's a big airport, you'd want to allow 15 mins from train arrival to being at arrivals (even at B'ham, you would need to allow that for the monorail). You might be lucky and get a train that arrived at 11.45, but that's unlikely - let's say it arrives at 11.30. That would mean it left at 11.10. You'd want to be on the platform for 11.05, meaning at the station by 11. And then you've got to get to the station - let's say it's a walk of 10 mins (guesswork - OP hasn't said). So you're leaving home at 10.50 latest.
After meeting OP, let's be generous and say the flight lands on time and she's through arrivals soon after 12. Probably the earliest train back is 12.30, getting in at 12.50, home at 1pm (not including the pet collection, so if you add that in, it's going to be 1.15 earliest).
So even with journey planner, and all elements slotting neatly into place, that's 2.5hrs, just to meet OP at the airport. I'd rather DH was at home making a nice meal, baking a cake etc (both of which my DH has done for me when I've been away, and I'd consider much nicer gestures than coming to meet me at the airport!)
If the flight is delayed (possible), and train times don't work out quite as neatly (likely), it's easily taking almost half a day for a momentary gesture. I'd struggle to see the benefit (to anyone) of that.
@Dweetfidilove - I know you didn't quote cost (or have a pet to collect en route), but OP referenced both of those things.