In terms of power, I entirely agree that modern cars usually have plenty. As always, you have expressed a technical and legal best practice answer to a question posed (well, assuming that you meant to write '..as long as the caravan does not weigh more than the cars permitted maximum towed weight..').
But there are some nuances and preferences, admittedly already fought over in quite a few other threads, but which I think are helpful to someone thinking about what towing vehicle to buy. Not just the specified and permitted maximum towed weight.
For towing, the torque characteristic of the motor is important; traditionally caravanners have liked diesel engines for their lowdown torque. Modern petrol engines can also be good (or terrible). If when you're driving it solo it feels gutless as you set off from the traffic lights or when you try to be brisk about pulling out from a junction, you're going to feel that much worse pulling a caravan as well. The characteristic of electric motors is also very good, just the range and public charging that worries people about towing. My opinion is that plug-in hybrid (PHEV) is great for towing and the best I've experienced.
Then also quite a big deal is the type of transmission - manual gearbox, torque convertor auto, dual clutch auto and these days a multitude of other novel arrangements. Traditionally, most caravanners have favoured automatic transmissions. However, these days most automatics are the dual clutch type and I harbour quite a dislike for those. Others may (and will!) disagree, but they can be jerky and notchy in low speed manoeuvring and the software can be slow to react when you need to join a gap in traffic. All a bit unpleasant and although it feels like you're driving an automatic its all a result of computer controlled slipping clutches. The thought of towing with a slipping clutch makes me wince. Having test driven a few different options, I came down quite firmly on my choice of the BMW 330e because they still use a torque convertor auto.