Can a child seat attached post-manufacture be as good an attachment as a manufacture installation?
TL;DR  I feel trailers are a safer option for small children, but the circumstances of your commute may mean that a trailer is not an option or is a huge inconvenience.  In that case, I believe that a mechanic installed child seat is/can be just as safe as a "factory" installed child seat and likely far less expensive than a new bike.  

I (personally) don't ever recommend that type of child seat.  Even expert cyclists can crash and since children are often not good at crashing (they don't have instincts to roll, etc) those seats worry me.  Accidents happen and those style of seats have never felt safe enough for a small child (let alone an infant).  Both of my children (now three and four) have been towed hundreds of miles in a trailer, which essentially encloses them in a roll cage.  I've had times I've slid off trails into snow banks, and a rear seat would forced a child's head under snow.  With a trailer, it simply tipped into the bank and had no ill effects.  

All that being said, I don't think their is really a difference between the factory installed model and a well built child seat installed by a good mechanic on a bike properly setup for a rear rack.  In your case, if you were looking at the money to purchase and entire new bike, I may consider simply purchasing a trailer which would work with many different bikes and possibly be of other use to you as well (some are convertible and can be used for non-cycling activities as well).  If money was an issue, I personally wouldn't differentiate between a factory installed model and a mechanic installed model.