I can see why Barty withdrew, but this is the second time in a row she has done that the week before a slam, and her third tournament in the past five to do that. Sevastova is pretty notorious for withdrawing. These players are not alone because it is a WTA-wide culture (my favorite is one of the worst), but the WTA desperately needs to do something about this habit because it is getting absolutely ridiculous. And I agree that the "get in the car and drive to Eastbourne" comment is also a bad look, although at least she entertained that possibility when many others wouldn't even do that.
Meanwhile Feliciano Lopez played five matches in two days at Queens, yet is on the Eastbourne OOP for tomorrow… Not that the ATP is perfect and he may still withdraw, but somehow the problem seems way less severe on that tour.
I wouldn't have any problem at all if Lopez were to withdraw. There are a number of mitigating circumstances: First, his very heavy match-load in the last few days at Queens that you highlighted. While he got a walkover from Delpo in R2, his last 3 singles matches were 3-setters, and the final against Simon featured some very long rallies (that's Gilles Simon for you ...). People speculated that had Andy Murray not been his doubles partner, he might well have pulled out of doubles, but of course he stuck with it, giving his all. Secondly, Eastbourne is only an ATP 250 for the men, while Queens was an ATP 500. Thirdly, Lopez is not seeded at Eastbourne. Fourthly, while he won Eastbourne only two years ago, and has a good record on grass, he wasn't considered a favourite at Queens this year, and so his success came as something of a surprise. Not so with Barty in Birmingham.
Oh, and Simon is (as I type this) also down to play at Eastbourne tomorrow, despite having played 5 x 3-setters at Queens - total time on court, c. 13 1/2 hours.