Why in the world would you say cruisers are obsolescent? While destroyers and frigates/escorts are the most common surface combatents today, Jeff Head correctly points out that some Japanese (and British!) "destroyers" are destroyers in name only, since they have the size, displacement and armament of a cruiser! Apparently, there is still a place for larger warships with greater range, duration and capability. Nobody thought that the Kirov was obsolete at the time, even though battle cruisers had been considered operationally extinct since the sinking of the Scharnhorst. If your naval stratagy calls for a cruiser to fulfill certain mission requirements REALISTICALLY, then the "cruiser" is relevant. The Slava in question falls into the niche left by the lack of Kirov battlecruisers and Kiev-class carriers, in that it can complement a carrier battlegroup, or as the Kievs were designed to do, guard a SSBN bastion. it has flexibility that a destroyer would be hard-put to match. just my opinion.
not really, kongo class is 7500 ton in standard load and 9500 ton in full load. Not that much larger than DDG-51. Type 45 is actually in the weight class of 052C. Whereas when you are talking about Slava class is 12500 tonne in full load. So, it's much larger. It seems to me that PLAN is trying to copy what USN does, which means it's going for something in the weight class of DDG-51 (so around 8000 to 9000 ton in full load). And as I mentionned before, Slava doesn't have that much better air defense than 051C (which is inferior to 052C) and its strike capability can be well compensated by a few datalinked type 22s.