I'm not sure this is much more satisfactory than your approach, but it appears to at least work and would adapt to different y axis ranges.
It's interesting that the 'ylimitmethod' and 'xlimitmethod' work differently for their default values of 'tickaligned'. Maybe because the x labels are outside the axis and thus have more room to be displayed.
x=-1:0.1:1;
plot(x,x,'o-')
grid on
ax=gca;
ax.YAxisLocation = 'origin';
set(ax,'fontsize',20)
yticks([-1 -0.5 0 0.5 1])
set(gca, 'ylimitmethod', 'padded')
% ylim([-2 2])
