Of 52 births that either occurred on-screen or we were told about contemporaneously, 34 (65%) took place in hospitals (including Marcus's Emergency Clinic, Dr Baker's Clinic, Sherman Falls, wherever Sonny was born, and Los Angeles). Some of these (I'm estimating 3) were hospital-focused stories (i.e., a one-named character giving birth).
Importantly, if you look at the last 10 years of story, there have been shockingly few births (7, or one every 17 months) on-screen or otherwise, with only 1 happening at SU Hospital and one at Dr Baker's clinic (28%).
Go back another 10 years, we have 17 births (or one every 14 months), of which 6 took place in a hospital (35%).
Go back to April, 1992 (halfway point of the show), and we have 24 births (one every 13 months), of which
9 (nine) took place in a hospital (38%). So it's not just our perception - they're actually getting worse at this and cheapening the "drama". (Note: This doesn't include Abby's current pregnancy.) A Salem character who is pregnant is twice as likely to give birth outside a hospital than inside.
Jennifer Rose Horton was in fact the first non-hospital birth, so I guess Abby's following dual traditions: the DiMera tradition of kidnapping pregnant women and the Bill-Horton-branch birthing-in-odd-places tradition, LOL.
[Edited to Add: This information does not include non-live births or information for Noah, Tate, or Emily, who basically need a category all to themselves and also weren't shown or discussed to be born in hospital.]
