By the time of the 24th century time and resources do not matter
Not true. It does matter, the Federation has a limited territory with limited amounts of materials and energy.
the Feds can design whatever they want and build whatever they want they have NO limitations.
Not true. They have every limitation. Their technology level, the amount of materials and energy available, the amount of manpower, you name it.
The Galaxy Class was one of the most if not THE most efficient ship in Starfleet due to the fact it was multi purpose.
Not true, it wasn't. It was power-hungry, didn't do any of it jobs as good as a dedicated vessel could have (which is why most starships are not multi-role at all) and was more of a statement then a tool.
What were the limitations of the Galaxy Class?? none whatsoever.
Not true, it's limitations where multifold. For example: The space used up for science labs made the amount of firepower it could dish out less. And the other way around; on multiple occasions we've heard mention of science vessels dispatching, especially designed for taking the best scans; those that the galaxy class couldn't.
What could other ships do that the galaxy Class couldn't??? NOTHING!
Not true. Escorts could dish out more firepower for their size. Science vessels could scan and analyse better and further. Carriers like the Akira could bring more fighters to the battlefield. Hospital ships could care for more wounded. Everything the Galaxy class could, another vessel could do better. It's only the fact that it could do everything in a basic capacity, that it was useful for exploring; so you don't have to move a whole fleet of vessels. As such it was efficient in only two things: materials and manpower.
Take a Galaxy Class ships basic requirements, add to it another warp core and lots more weapons and defences, give a new better design and you've got the most efficient ship possible and you have zero limitations and it can do whatever any other ship can do.
Not true. If you did that, you'd simply have a Galaxy Class ship with a new design (which, in effect, makes it another class of ship), more weapons and defences (and thus either more volume and energy-consumption or less science labs) and it's limitations are even bigger then the original.
You could even have a ship as efficient as a Galaxy but nowhere near as big, the Galaxy was for carrying families so build a ship that doesn't carry families and you probably cut the size of it by one third and make it a more agile ship.
That is the only thing you've said that has any basis in truth. But then it wouldn't be as multi-purpose anymore. Strip away things like that and you'd simply have a specialized vessel, which is unsuitable for exploring by it's own.
Give it up; in order for your question to make any kind of sense is to define that question. "Efficiency" isn't an overall concept, it's applicable to any number of things; choose one. If you don't, this is not a real discussion; it becomes a fanboy wank dream. And I'd rather wank on my girlfriend then on some silly boy fantasy.