why the fock would we need battleships in a modern day war

Battleships, I don't know, but Carriers are an essential force of any modern navy, due their ability to produce +350E when switched off.

because on is for the radar?

In ~1915 Ford could make one Model T car ("Tin Lizzy") every 5 minutes. Assembling only took a few hours.
Today a car takes ~2 days to build I think. Depends of different factors of course. A few weeks for a T-34 tank sounds realistic. Maybe even faster (days?) if they had had trained workers instead of old men, children, women...

Titanic, USS Enterprise (american carrier in ww2) and Tirpitz (largest german battleship in ww2) took around 2 years to build.

Then there are those "Liberty"-ships the Allies had in WW2. Spamable freightships designed to be build as fast & cheap as possible. They took 8 months to build.

Today there are much better productiontechnics but there is also much more stuff in each tank/plane/ship. Like electronics and a nuclear reactor. So I think even today a warship takes 1-2 years to build...