Just by keeping that money in a savings account you'd save something.

The price of the phone and the installment amounts are fixed at purchase. If there is a positive inflation rate you are guaranteed to make a real saving (but not a nominal one) by paying some of the purchase amount later on. What happens to your salary or the price of the phone later has nothing to do with it.

Or if there was literally anything else he'd prefer to buy up front than wait until he'd saved up enough to replace the cost of the phone.

He can't predict the future. The relevant metric must be

1. The chance, weighted by amount, of a price hike/salary increase

2. The chance, weighted by amount, of a price decline/salary decrease.

As inflation is generally an upward trend, clearly no. 1 is more likely and thus the best bet.

Another advantage of financing even though you would have had the money on hand is that you have more liquidity/the option of doing something with that money in the meantime.

Also someone may have some assets they could turn into liquid cash if I really needed to but may not have a lot of liquid cash on hand, so there would be little risk in paying something in installments as long as their assets would be enough to cover it in a pinch.

While liquidity is a reasonable argument, I only know this from "rich people doing things/investments"; e.g. not selling shares in your company when building a new house, or a company building a warehouse.

I am not sure it actually applies to the cost of a phone. Chances are, if those matter, you'd be better off with a cheaper phone to begin with. (Substitute phone with other luxury articles).