Can I make this caramel the "usual" way instead of using golden syrup and condensed milk
With millionaire's shortbread you need a caramel with the right consistency, it needs to be soft enough to cut through (and chew) but have enough resistance not to squish out. The golden syrup, condensed milk and butter recipe comes out with just the right consistency, is extremely reliable and easy to make which is why it is popular. 

There's no reason you can't make your own caramel, you just have to make sure you don't get the end result too soft or hard.