It will be the case that most (notice that I say most and not all) who buy upfront are financially more secure, than those buying on finance deals. By financially secure, I dont necessarily mean with the highest incomes, but those with the most equity and lowest debt in relation to income and outgoings.
The cheapest long term option for car ownership is buying outright. Those who can afford this usually do it. Some go for new, but as lots on this thread say, lots are happy with 2-3 year old models bought outright as a really good value way of getting reliable cars with latest features. It does mean those people aren't always driving a less than 3 year old car.....but generally they don't care about that.
People buying on finance are usually doing it because they can't afford the big upfront payments of buying outright. By buying on finance or via plans, they often end up getting a new car every 3 years. That wasn't why they went into the schemes but is one of the effects and after they've had that, they can believe that anything older is bad and unreliable and that they 'need' new every 3 years. The fact they have got new every 3 years helps them justify the much higher overall costs of using finance.
OP clearly understood that having to use finance rather than using the balloon payment and then avoiding monthly payments was the cheaper long term option, but feels it's not affordable right now as savings depleted. This will cost her more in the long run, but she feels she's lacking in choices. That's the reality for lots of people....they dot have the choice due to lack of large sums of money stashed away, so have to go for the more expensive option. The car companies have cleverly made it attractive and not seem like the option for those with less financial security but something to aim for that is aspirational in terms of new cars regularly....but for the car companies of course it's a way to keep selling more new cars. It's very clever.
Someone made a good point to Op that she might have no choice now, but could aim to get the 2nd car off finance and buy it rather than start a new finance deal when the balloon payment is due. That's a good idea. Reducing from 2 cars to 1 on finance will save money over the longer term and mean there will only rare rely be a need for a lump sum of money, rather than it happening twice in the cycle.
Lots of people could choose to buy at the end of their finance cycle (not with lease schemes) and plan to do so, but get lured I. With a seeming good deal and the chance if another new car and lots of guff about 3 year old cars needing lots of money spent in them. And then they're in a seeming eternity of always paying monthly. Yes, it's affordable on a monthly basis, but you pay much more over time. It depends if you're interested in spending less on cars over the long term, or living just in the here and now.
Those who have no choice but to buy on finance, often lack security in other areas of their life too. If the boiler breaks and requires £3k it will be hard for lots of people, or if they need to find another big expense, or lose their job, they can quickly be in real problems. But those people often have a new car and a new sofa etc.
It's a financial step change to not just look at monthly affordability but long term costs and it's a step hanged for many to save any surplus and spend so there is a surplus, so I'm a year or 2 monthly payments can be a thing if the past. Not possible for those in very low incomes, but lots could make the step change if they thought about it and planned. They could save thousands over the years.