I'd say always follow the "simple, brief, and spiritually uplifting" guidance, and as mentioned use the items listed in the "may" bullet points as the baseline. If it's a service with multiple people being baptized, a welcome from different organizations might not allow for simple and brief. Or if it's a child who's been attending Primary for a while (whether child-of-record or maybe a 10-year-old), perhaps the welcome would work better during second hour the following Sunday. But I'm certain there's cases where a new member would be greatly blessed by a brief welcome from their organization leader during the baptismal service, and I agree there's nothing stating this cannot occur. And the Bishop might have to be brave and suggest to the Relief Society they present their keepsake memento to a new sister after and not during the service (the EQ generally isn't as thoughtful...)!
As an aside, I interpret the "A brief welcome from the brother who is conducting the service", as a general welcome to all those in attendance, and not a specific welcome to the person(s) being baptized.