This particular thing was actually tried by the Soviets. Farms were considered excesses of kulaks. Kolhos (collective "farm") was the replacement.
And yes, it was possible to say "my kolhoz" like people say "my city", good point. Even if "our kolhoz" was a lot more accepted, since it emphasizes how collective it is.
It is also possible to feel personal affinity to collectively owned space.
The difference between usually implied individual "my farm" and collective "my farm" is of course in the governance.
Collective ownership may end up being governed by ineffective unaccountable and irresponsible "people representatives". E.g. deciding that genetics is a capitalist plot, and planting corn everywhere is the solution to all problems (both cases actually happened on a massive scale).
The result is not very different from what ineffective unaccountable and irresponsible large capitalist landowners do.
Both systems disenfranchise the disadvantaged ones, since decisions can practically never be completely unanimous.
So it's good if you agree with the party line, but if not - violent suppression comes, no teaching on the farm.
That's where the feeling of "my farm" breaks down. On a private farm you have a lot more options before you are lost.
I get the challenges with governance in capitalism-turining-feodalism which we have now in many cases.
But I do not get it why people imagine that full collective ownership is a good and sustainable alternative.