do the mobile companies actively target under 65's at the end of contract for a new phone and not contact over 65's on purpose to make more money?
Can't speak for telcos, but I can speak from experience of a related customer service business, where the initial good deals are all time limited. If the initial deal is a good offer for customers, then its loss making or profit neutral for the provider - these offers are called "acquisition tariffs" and they're frequently not offered to existing customers. The maths is that you incur customer acquisition costs, you offer a loss making or profit neutral deal, but make your margin from that smaller proportion of customers who stay with you on worse terms when the contract expires. In mobile, that's by keeping the tariff the same when the contract ends, in energy or broadband it is by retiring the acquisition tariff and only offering higher price deals, in both cases accepting the churn.
In these markets, there is definitely no attempt to preferentially target existing customers with the really good offers, because otherwise you'd never make any money. If you have a segment you believe will be more likely to churn out to a competitor, the norm is to actively offer them a deal to stay eg via email or outbound sales calls, but not as good a deal as the acquisition tariff. For any segment where there's less likelihood of churn, you still offer deals, but only passively (eg through the web site). Those passive deals won't be very good at all, probably worse than the proactively promoted offers, but there's better offers to be had if those customers phone up to cancel. Even then, these customers will still struggle to get the best deal by staying with their current retail services provider, be that phones, broadband, energy, insurance, or home services.
In practice, this does mean the offers work as though segmented by age and socio economic group, and the companies know that, and don't mind. However, IME management are very wary of doing anything directly off those forms of segmentation, they could be clobbered both legally and reputationally if it leaked out, because it could be seen as various categories of discrimination. The sort of cost of being caught doing the wrong thing there would be of the order of several hundred million pounds for a large retailer. Incidentally, that's why the government are progressively intervening in the energy market, because it is the older, poorer customers who generate most of the profits, as the CMA enquiry found, although it was widely known before. There is of course a consequence of calling this a "broken market" and fixing it, that the good deals for people who shop around will vanish, because the companies can't rely on the inertia of disengaged customers. You may see that as a good thing, but if that's the case, don't complain when your energy or airtime bill goes up by 25%. Despite what the tabloids claim, most of these companies aren't making excess margins, so they'd need to earn the same profits more broadly spread across the customer base.