The Constitution class was probably Starfleet's main "do it all", self-sufficient platform. Which, while being older than some others, made it a special command with more freedom than other platforms.
Yeah and only Captained by those who are on the fast track for the Admiralty, 5 year missions are good for the career it seems.
The Discovery is a great ship but it is more of a technology testing/training platform than anything else, crewed with mostly scientists, engineers and cadets.
Its not meant for front line work or true exploration due to how secret the spore drive is.
Whereas the Constitution class ships are front line heavy cruisers designed for long periods away from known space, it has the engines, warp core and offense/defense systems all designed around that purpose on a platform that is big enough to hold the crew and supplies it needs for a 5 year mission.
All the technology on-board needs to be tried, tested and certified or it isnt installed in the first place.
With that being said I still think they should have repaired the Vengeance, painted it white and called it the Enterprise A, first of the Federation Battleships/Explorers to really emphasise the departure from the PU.
A platform of that size would provide so many options technology wise, the automation would help as well added to the much improved engines as we saw in the film,
Truth is having a bigger ship does give you more options, personally I have always thought the D'Deridex Warbirds were excellent ships big enough to serve as a multi role platform although the increased size did hurt their top speed, the increased size and especially volume meant the Enterprise D was a step in the right direction but it didnt last.
Bottom line for me is that the 600+m Kelvin Enterprise is much more believable as a Deep Space Explorer going on 5 year missions than a 300m could ever be.