"The whole family would want to see him badly at this gorgeous stage." I doubt they would. That is what we as parents think about our precious little ones.
Few parents have the sense to leave an event if their children turn into the center of attention due to grizzly, whining, ear piercing noises and screams. Every time their kids quieten down for a moment and settle for a second they think "piuh, finally quiet, we can stay", and a minute later when the screaming/whining/grizzling start again, they think "if she/he does not quieten down in the next minute or so, I will leave" subjecting all around to frazzled mum bouncing, feeding, giving drinks, toys, other guests hair or mobile phone "just for a second" for child to slobber all over "just until child settles" and so subject other guests to an event where a childs presence is the center of attention as everybody attention is on "when will they manage to get the child to sleep/eat/drinnk/play quietly, rather than enjoying the event.
I would say that the reason most B&Gs opt for childfree weddings is because parents are just totally blinkered as to the effect their moaning/frazzles child has on the event, they think they are the only one struggling and nobody notices, but it does in fact ruin the event.
People just cant take the risk, so they rather not invite kids than having the most expensive party ever ruining by constant Squeeees and screams.
I needed yesterday to be reminded of this stage of a childs life.