IMHO the best option for inputting a small integer value is the combination of a text field and a stepper, which has been around for a long time and has its own name (for touchscreen operation, the +/- buttons could be made larger and horizontally, like the steppers shown):
For dates, a calendar control would probably be appropriate.
I'm a bit puzzled as to why dropdowns are a "4 tap operation" - once to dropdown and once to select, with possibly some intervening scrolling if it's a lengthy list. Where are the extra 2 taps coming from...?
Calendars are certainly not appropriate for dates of birth, lest anyone get that idea …
Calendars are useful when entering recent dates you may not perfectly remember (i.e. you might know that the day you want was a Monday last week, but you might not know the exact date) or for planning (i.e. you might know that you want to depart on some Saturday in September), especially when either days of the week or dates might be relevant points of reference for you.
For dates very far in the past that tends to break down a bit, though, depending on the exact use case. Calendars are cumbersome to navigate if you want to go back years and years.
For either, you can just enlarge the widgets to enlarge the click areas.
For spinners, one can often scroll one's mousewheel (or equivalent gesture) with the pointer inside the spinner to rapidly increase or decrease the value contained within.
The best calendar widgets I've seen also permit you to click a part of the widget -say the displayed date- to type in a desired date.
>I'm a bit puzzled as to why dropdowns are a "4 tap operation"
Either they count 'moving on' as a tap, or they just assume that on average you scroll at least twice: "First tap the control, then scroll (usually more than once), find & select your target, and finally move on."
It might depend on the length of list, and phone and browser, but a quick swipe usually starts it scrolling down, and a quick tap will stop it (there's usually some momentum, it'll stop itself eventually too).
For a short scroll then a single hold and swipe will work.
IMO the best choice for a calendar is three separate boxes clearly labeled "MM", "DD", and "YYYY" in some order, preferably with the property that once the second (or fourth) character is typed, the cursor is automatically tabbed over to the next box.
On iOS I could three steps:
1. tap dropdown to select
2. scroll list
3. tap 'Done'
But with any list of significant length (the reason you would use a dropdown in the first place) you'll probably need a few actions to scroll to the right item.
Only if you know the options in advance as the sibling comment says.
And mostly for very significant length (e.g. "all my songs") E.g. for up to 20-30 items dropdown is still better, and you can select with one finger without much concetration.
Of course there's also the "searchable dropdown", or a dropdown where you can type the first letter(s) of an options to jump there.
Not really. If you don't know what you're looking for, search with instant feedback wont work, because while you might find something, you don't know if you missed a better option (under another starting letter or substring).
https://en.wikipedia.org/wiki/Spinner_(computing)
For dates, a calendar control would probably be appropriate.
I'm a bit puzzled as to why dropdowns are a "4 tap operation" - once to dropdown and once to select, with possibly some intervening scrolling if it's a lengthy list. Where are the extra 2 taps coming from...?