Yes, the move towards "Wash and Wear",along movement away from many natural fiber fabrics hastened the decline of ironers, but ironing (by hand or machine), as well. Also even with a dryer, many items still had to be ironed such as table and bed linens, shirts, jeans, etc, but as you say today there is a different standard. Today also at least most urban areas have lots of drycleaners/laundry services that do shirts for about $1 or $2 a piece, so many wives and most men are happy to sent their shirts out.
Paper napkins replaced linen/cotton, tablecloths are rarely seen except at special times,and even then they are likely to be polyester (as with napkins).
Also consider many women work outside the home, something that was rare in the 1950's and 1960's, thus do not have the time to devote to "housekeeping", including ironing as their mothers/grandmothers.Also many women had a daily or live in cleaner (help was cheap), so there was more than one person to spread the housework about. Well that is if Madame did any of it herself. If not, then it was all up to the "girl", but many coped quite well.
Ironers are once again popular because many people are using high thread count linens again, and or collecting/using vintage linens, all of which must be ironed. A good French hand laundry service is expensive, and "help" even more so, so a mangle is a better option.