Ultimately, it's up to you. If you want to get to your event on time I suppose it depends on your appetite for creating hassle that could be easily avoided. Personally, I prefer a relaxed approach with some confidence. And minimum (note that specific word) connections times are intended to be the shortest time for a connection, not the longest otherwise they would be called maximum connection times.
Yeah it's a case of which itinerary I print. I will almost certainly take an earlier train, I simply want to establish what my final deadline is to be at Slade Green station and on the London-bound platform, after which any failure to make my connection at Kings Cross would be my fault rather than the rail industry's. Turns out it is 10.22 and that's the itinerary I will print.
If I'm ahead of it, which I will be, the service patterns are such that there will always be a valid itinerary that arrives at St Pancras at or before 11.05. Trains aren't overtaking each other at any point along my planned route.
In general I do, like anyone, try to balance allowing plenty of time and reducing stress on long journeys against having a reasonable journey time. By allowing less slack than some people, I have benefited from faster journeys and saved a lot of travel time in door-to-door terms over the years, compared to them. The trade-off is I may occasionally miss a connection that they would have made. As a result of frequenting this forum in recent years I have, at least, learned the importance of making sure I'm always travelling on a valid itinerary.
I do think having really high minimum connection times like 31 minutes for arriving at St Pancras and leaving Kings Cross (or vice versa, which is even crazier) has an adverse effect on end-to-end journey times generated by those journey planners that do this, which risks encouraging people who may be thinking of taking the train, when they see how long the train journey will take, to opt to drive. Furthermore it's hard to see the justification for saying a transfer from Thameslink to EMR at St Pancras requires 15 minutes, but if the train leaves from across the road then you need 31 minutes. There's no logic to that.