I certainly think there's merit in charging capital gains tax on everything, including your home, but bring back either time apportionment, tapering, or indexation allowance, so that the longer your own your home and it's going up in value, there's some kind of mitigation of the capital gain.
Make it so that someone making a windfall killing of £100k be sheer luck when they buy and sell a house within a year or two due to area improvement, a new railway station, or whatever pays CGT. Whereas someone who's had a home for 40 years and it's basically just gone up in value in line with the market pays a minimal amount, relief having been given either "per year of ownership" or based on general inflation, or based on house price inflation, etc.
Likewise with a business. The longer you own and grow a business, the more relief you get when you come to sell it at a profit. Whereas if you just "luck out" and make a killing in a year or two, the relief will be minimal and you'll pay CGT on most of the profit.
Like I say, we used to have this kind of relief, being taper relief, or indexation allowance, etc., but in the last 20-30 years, we've morphed away from that to just generally lower rates of tax with no reliefs for time owned nor inflation.