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Yeah, batteries are always going to be a cost issue, I guess if you can spread them across multiple tools its not so painful, I roughly have 1 battery per tool I think, but i'm rarely using all the tools at once. I have Makita, and the fast charger is excellent, so even if I do run out it's only a 20 min wait.
Another thing to consider could be dropping down to 10 to 14v if it is only for low intensity, occasional use. I bought my wife a 10v Makita impact and drill to keep in the house, and its great stuff, really lightweight, but enough power to drill a 12mm hole in masonry with no issues at all, and the impact is perfect for ikea furniture...
In a nutshell, yes. unless you are going to be doing some really heavy work, or want to save a little money, I would think cordless meets most requirements. For me there are still some tools where I am not willing to go cordless quite yet, big things like chop saw, table saw, but thats mainly because I don't move them round very often. But for drills, impact drivers, circ saws, grinders etc I would go cordless. Pick a battery system and stick with it. You won't go wrong with Makita, Milwaukee, DeWalt, Bosch blue at the upper end for DIY, or if you are on a tighter budget brands like Erbauer do really decent stuff for the money. I mean for 90% of people the Lidl Parkside or Aldi Ferrex stuff is probably more than good enough.