I'm not sure that conquest needs to be made any easier, it's already pretty straightforward to take 2 cities or 1 city + vassalize two of your neighbours before the end of Classical. But you do need to have high initial warscore, some territory demands, win decisive battles instead of just a bunch of skirmishes, and capture 1-2 cities. This all takes some prep work and conscious effort but is all achievable. You shouldn't really be able to annex an entire culture because they were oppressing your religion in a single neighbouring province or because they attacked one of your scouts one time 300 years ago.
If anything you should need a demand on a city to be able to take it in a war, or suffer a massive and long lasting %-based stability hit - i.e. that city should be at serious risk of rebels and bad events for the next 30+ turns, that you can't just avoid by building an aqueduct and an extra Commons Quarter.