I replied "in my pocket turned off", but that's kind of wrong. I leave it on in DND mode. I use Golfshot on my phone, so the phone is on but will not ring -- unless someone calls me twice in a row (it better be important!), in which case it will vibrate.
I was playing one of the courses at Rockleigh in NJ, and same deal -- really short grass apron leading to the green. I was about 15 yards away and even slightly uphill. This was early in my golf life before I had even a semi-decent short game, so I decided to putt up to the green. Well I'll be damned, I sank the putt!
If you were hitting 75 full swings without some sort of break, yeah, you probably got tired. Looking at your HC of 30, if you average just over 2 putts per round, 75 full / wedge swings is a full 18 holes of golf.
You really need to do both, and playing a course teaches you things such as course management which you can't get from a range. That and actually seeing the results of that 50 yard pitch as it hits a green, and the fact that the practice green is only 1 green, and there is a lot of difference between that and the 18 on the course, so yes, you're missing a lot if you're not out there playing.
I'll never forget playing Ardsley last year. Classic Westchester NY country club. Member sends me and a friend ahead to the clubhouse, says grab a beer and lunch on the terrace. My friend is in cargo-like shorts (should have had more appropriate clothes since he was out here on our annual golf outing -- this was a pre-outing round) and sandals. Member figures he'd get away with the shorts, but I lend him sneakers. Member also says "tuck your shirts in", my friend kind...
62 for 9 holes is not bad for a rank novice. The first time I actually kept a true score on a real course, which I did primarily for a starting reference point, I shot a 65. I've so far knocked 10 strokes off of that, so yeah, you did fine.
Keep in mind that only about half of your average recreational golfers (especially those who only play a few times a year) break 100 consistently.