It appears a number of people in this thread have failed to understand that this is the problem I'm criticising: Bladesinger is a full mage (with better AC and Concentration saves and Acrobatics and mobility) who can also rush into melee as a competent melee type.
The bladesinger isn't really a full mage with benefits though in comparison to the other wizard subclasses. It is very front loaded so it might seem this way at lower levels but its melee ability drops off fairly quickly at mid levels and what you often end up with is a wizard that's hard to hit. Other wizards are getting various additional abilities which can be used to deal with a wider variety of situations.
For me the bladesinger is strong at low levels but worse than several of the other wizard subclasses at higher levels. Maybe that's a design problem but other classes have this issue too.