You are probably right about the grass and sprinklers. .
There are options in regards to the grass, depending on why it's failing.
I see 2 failed spots in the photos on this page, one is along the top of one of the berms.
As this is unlikely to be a desire line (people made pathway) that's causing the fail, it's likey a drainage issue related to the berm.
Assuming no appetite to dig up the berm and revisit the soil composition, I would suggest substituting the Kentucky Blue Grass (which is what 95% of all sod is) with a drought-tolerate ornamental grass.
This would look terrific and avoid the cost of irrigation or changing up the soil.
In regards to the patch of dead grass on the flatter, larger section towards to the western side of the park, that looks more like compaction/overuse.
That would afford 2 choices. One is as suggested by some, harsdcaping the area
While that could be done, I'm not sure it's necessary or the prettiest choice.
The other is to substitute the sod for something people will choose not to walk over.
This could be a spot for a signature annual flower bed, which could be changed up for every season.
One could also split the difference I suppose and create a narrow path of paving stones w/new landscaping to one side.
But i think I would go w/a flower bed or landscape feature, and I would block off the entry point with additional seating (bench)
I would like to see the flower bed mimic the fountain with 3 well defined tiers, each edged w/stone mimicing the style chosen for the fountain.
Then layer up for a summer featuring bright purple trailing petunias falling over the edge of the first layer, backed by white snap dragons; followed by ageratum (a low blue flower) backed by by bright Red Snap Dragons.
Then finish w/something big, robust and pink w/phosphorescent green leaves around it, maybe sweet potato vine.
Just my 2 cents.