Could simply inviting him and asking him to do a reading or something have been a better idea.
Better for who? Certainly not the bride.
If it's mum and stepdad who are the ones involved in her daily life and have met the groom's parents, this sort of sidelining for a never very present uncle will have people questioning her relationship with her step dad as they are on here.
Maybe, given that the bride has never called or referred to her step-dad as dad and she’s close enough to her father’s side to have both her other half-sister and cousin as bridesmaids they’ll just be more aware of the relationship between them than the OP is. Especially as even the OP described the relationship between the bride and her step-father as “they got on”. Not even “they’re close” or “they’ve always been like father and daughter”.
The OP dismissed the other family relationship as Christmases and birthdays only, but given the sister is presumably older than the OP and the OP herself is married how could she possibly know the ins and outs of the relationships over their adult years?
Op has said they're all going to the wedding, noone's suggesting otherwise but I do think Op isn't unreasonable to feel concerned, particularly about her Mum's feelings actually.
Might be nice if she had a single concern about her sister’s feelings though...
And the OP did suggest she didn’t want to go to the wedding