I remember as a child we had dry cleaning picked up and delivered weekly, not only for my dad's shirts but also for things like sheets, before those were permanent-press. The cleaning always came in brown-paper packages, a relic of an earlier age.
Previous neighbors of mine, both city executives, still had their dry cleaning delivered weekly, as recently as a couple of years ago. But they had a maid at home to receive it ...
I would have thought the incidence of dry cleaning had probably gone down a lot in more recent decades for several reasons.
One is that clothing has become generally much more casual, in business as well as elsewhere in daily life. In smaller local businesses, tech firms, hospitals, government, etc., men now don't often wear a jacket or tie, and women don't often wear skirts or hose. The more formal business dress style seems to endure mainly in large corporate offices and among 'serious' professions like lawyers and accountants. Even people who office in city skyscrapers may dress down on some days, when they don't have to meet with any clients.
A related factor is climate change and demographics. In the US, the population has moved in great waves from northern to southern states, where full wool tailored suits etc. are a lot less comfortable as daily business wear much of the year. In some states, like Hawaii, apparently even lawyers seldom put on a suit except to appear in court.
Another factor is that you can now get decent permanent-press fabrics that still have a reasonable percentage of cotton, not only 100% polyester like in earlier decades, which tends to look cheaper and flimsier. I personally would never buy something that had to be dry-cleaned unless it was something like an outer coat, jacket, or sweater that rarely needed cleaning. (I have enough trouble nowadays finding anything except flimsy Asian fabrics that say wash only in cold water. Whatever happened to decent, heavyweight 100% cotton denim jeans with no stretch and no cheapo streaky dye job? But I digress.)
A related reason is that there aren't as many stay-at-home wives, or maids, who are willing to iron all the shirts of the man of the house. When there were more slaves *ahem* available, it was easier for men to just expect someone else to do the work, which it has to be said is tedious and slow. At least now men who wear dress shirts are often willing to either iron them themselves or (after they find out how much time that takes) take them to the cleaners and pay for the cleaning themselves.
The entry of women into the workforce has been a big demographic change, not only in that women are less willing to iron men's shirts, but that they too have more clothes that need to be dry-cleaned and less time in which to iron. In general, women's work has led to a huge surge in the service economy, with other people now doing things for pay that women used to do for free at home. Dry cleaning is only one of those jobs, often taken by immigrants.
It may also be partly a class issue now whether people can afford to have someone else do their dry cleaning. As more people work longer hours and live in cities or suburbs, there are indeed more dry cleaners in every strip mall, and the price of having a few pieces of clothing dry-cleaned occasionally has become low enough that middle-class employees can afford it. However, because upper-middle-class suit wearers need almost every shirt and suit dry-cleaned every week, the cost for them is high enough that you almost need a higher-paying job to be able to afford the cleaning.
Fortunately I very seldom have to wear clothing that formal these days, but if I did, I might hesitate to have it cleaned for one reason: I would probably forget ever to pick it up. I lost a really nice shirt that way once. \-: