As DM flying J
- FCL access
- likely to get first choice of meal

Better support when irregularities as stated
Better chances of op-up to F when available and oversold

In general: yes, there will be some perks but overall J is already a major step up even without status.

Ever since I started to fly LH mainly in J cabin I`ve become less loyal to an airline/alliance and pick flights based on schedule and then price (although I still seem to fly OW more often than any other alliance, just less on CX than before)