What is currently the ultimate or the best multi-role warship class aside from the old battleships and existing aircraft carriers and amphibious assault ships? A warship that can do all missions: naval supremacy, anti-submarine warfare, air defense, etc. A warship that can sustain all the navy's needs in defending a country's sovereignty and force projection when there is a pending threat from foreign modern navies. A warship that can stand on its own and live on the sea for a long time. A warship of your dreams that no matter it gets attacked by a nuclear submarine, a fast destroyer, a supersonic fighter-bomber, rapid-firing guns and guided missiles all at the same time... it will still survive and probably win the fight!
A Super Star Destoyer. If it was good enough for Darth Vader, it is good enough for that.
Seriously though, there is not real such thing as "the best", particularly in a situation like this.
A good crew with a mediocre vessel will often, perhaps even usually, be able to defeat a good vessel with a mediocre crew.
Now, if someone wishes to come up with a vessel capable of meeting ASuW, Area Air Defence, Land Attack and ASW operations needs, that can certainly be done. However, the more major roles a vessel has, the greater the amount of required equipment and crew, which increases both the cost and size of the vessel. And if all such roles are "packed" into a single vessel, instead of being somewhat more evenly distributed across a number of platforms, that reduces the available footprint of a navy. This becomes even more of an issue when upgrades and maintenance are considered, since that can occupy a third of a naval force at any given moment. By increasing the size, cost and complexity of the vessels, it can have an overall positive impact of fleet capability, but also achieve a negative impact on fleet numbers. This leads to situations where some deployments or patrols just cannot be conducted due to a lack of ships.
Interestingly, this also can increase the risk to a navy or task force, since each ship have greater importance, more care must be taken, less vessels be lost. In effect, the vessels could end up not being deployed in situations where they could be useful due to concerns about the vessels coming under fire, or be damaged or otherwise lost.
Now, if different vessels work together within a task force to meet the overall task force mission requirements, there is an overall reduced and distributed risk, as well as different elements of a task force being able to support one another.
As I hope I have illustrated attempting to achieve what you seem to desire in warship capability is not an easy task, as issues appear and intersect at a number of different levels. This is also without any consideration to in what sort of environment one would be operating is. Open ocean/blue water fleet ops is quite different from what can (or should) be done in more restricted or littoral waterways
-Cheers