The only FOO is the gunner. He shoots at what he can see, and cannot shoot at what he cannot see.Not in my field of knowledge so treat these comments as queries rather than answers...
If the troops were lying on a reverse slope or in dead ground, they'd be doubly protected. Firstly, they wouldn't be seen and therefore not identified as targets. Secondly, direct fire would pass over them.
Assuming that the FOO would be located in the vicinity of the guns for ease of communication, two limitations come to mind. Firstly, fall of shot beyond the crest of a hill or mound wouldn't be observed so adjustment for range would be hit or miss - with the emphasis on miss. Secondly, the FOO wouldn't be in a position to adjust fire if the troops moved. The guns would be firing at a vacated area.
The ability of the modern FOO to view obliquely and communicate from anywhere on the battlefield is a definite force multiplier.
Then add in the absence of maps with grid squares and you're left with the artillery firing in the general direction of their enemy rather than aiming at them.
I don't think that it's fair to compare land artillery with naval artillery. Aside from different tactics, the Navy didn't have to contend with dead ground and organising the supply train when they shifted location. I don't know whether the artillery had to move during their engagement but if they did, the move would have been rather more involved than just hitching the guns to horses (organise the supply train, select route, prepare ground, etc.) and would have taken them out of the OOB for several hours.
During the ECW, the draught teams and ordnance train are civilians. They will deliver the guns to the battlefield, drop off the ammunition, then retire to the pub. If their side wins, they will pop back to collect the gun. This remained the case until the early 18th century. If the gunners want to move the gun, they will have to push it. Obviously not an option with anything other than the smallest pieces. Gustav Adolph (as he was always called until 1939 led to the Swedes suddenly preferring the posh Latin Gustavus Adolphus for some odd reason...) went for his so called leather guns, with lightweight barrels relying on leather wrappings for "integrity" (yeah, no thanks), which could be manhandled alongside the infantry - think Wombat... and yes, galloper guns came along. Problem was that all these, if they could be light enough to be mobile, rarely had enough punch to make a big difference. That only came along with the formation of proper horse artillery, with military teams able to move at high speed, deploy painfully close to the enemy, and ape the OTT dress of the posh blokes in the cavalry.