Yes, this is true. Many series are one person’s creative vision, and I think that elevates the quality of the storylines - it’s very normal for us to know who the writer is, they are often household names and people will look out for new series by writers they like. I think UK TV series are often more like self-contained plays than long running series with no end in sight (Dr Who excepted).
A very early example that was unique in other ways. Some shows had them, sure. But not as a rule. The ones I can think of were half-hour sitcoms like The Danny Thomas Show (the courtship of his older daughter), The Farmer’s Daughter (the blossoming romance between the two leads), and The Beverly Hillbillies (which seemed to start a new one at least once a year).
I can’t think of any hour-long dramas built exclusively around story arcs in the 1960s—70s the way 24, ST: Enterprise, and Highlander were in the '90s—early 2000s, but maybe I wasn’t watching the right shows…
One of the pluses is that actors have the chance to do other projects between seasons. A lot of time in a long-running series you can see them just going through the motions.
The downside is the extended time between seasons. Two years? Really? I watched the first two seasons of Hanna on Amazon and just by accident found out there was a third.
Long-running shows like Z-Cars, in the 1960s, had much longer runs - sixth months thru much of the '60s, and by the 1970s it was running more or less continuously.
It blew my mind when I saw the police show The Bill has 2,425 episodes. And I thought Law & Order had a lot of episodes!
I read about an episode of Doctors the other day that has a woman who thinks she being stalked by Joe Pasquale because she sees every person as having his face. (Joe Pasquale is a slightly old-fashioned comedian with a squeaky voice, and Doctors is generally a standard medical drama).
Looking it up, it turns out it’s episode 81 of season 21. 
Something that’s changed with the increase in filmic quality of TV is how long it takes for an episode to be made. It used to be that you could knock out an action drama like The A-Team or Wonder Woman in five weekdays. Now it’s more typical for it to take eight to ten days. That means a 26 episode season which used to take six months to film, is now a 22 episode season taking nine months. A thirteen episode season, which is becoming more common, means some actors can work on other projects within their year.
That’s America, but it’s also true in the UK nowadays. An episode of an expensive show like Downton Abbey has more in common with a contemporary American shooting schedule than a 70s UK schedule. It may be nine episodes long, but it would take five to six months to get it done.
I was going to mention The Bill. My wife is a big fan of that show (most of the episodes are on YouTube).
Some seasons have more than 100 episodes! As I understand it, it was often broadcast year-round, and aired several episodes per week.
Even those only had 13 or less episode per season. ISTM that the era of 20+ episodes per season is pretty much over, except maybe for sitcoms. All the prestige drama shows that people talk about generally have between 10-13 episodes each season.