Before the costs exploded, the Constellation class frigates would have been half the cost of Burke. There are jobs that need a warship, like patrol off Yemen, but the LCS don't have the defenses.
Also, this is not a good sign for Navy ability to build the DDG(X) which will be the successor to the Burkes.
Its air defense would have been pretty potent. It had the same Aegis system as Burke. The only limitation is it had the medium range Standard instead of the long range one.
The big recent change in naval warfare is that anti-ship missiles have gotten common. Ukraine used locally built ones to sink a Russian cruiser. Yemen and Iran have been making them.
Maybe try modifying someone else's again!
Semi-seriously, the Aus versions of the Type 26 (Hunter class) may actually be a good start: it has Aegis Combat System integration (albeit not via RTX) and a larger mast for the SPYs already as RAN needed those changes from the stock Type 26.
It (Type 26) also has better protection and safety than other European designs due to RN design standards being a lot closer to USN ones (and a lot of the modifications to FREMM were related to that).