My father was PR for DFDS from the 1960s to 1980s so we travelled on the ferries regularly in those days, starting with the Kronprins Frederik, then the England and the Winston Churchill, and finally the Dana Regina and Dana Anglia. These were beautiful ships (for proof, check out Bruce Peter's books on them), with wonderful food and good service. No expense was spared, with furniture and fittings by top Danish designers and limited edition prints in the cabins.
Even in the 80s it was recognised that the crossing was quite expensive compared with a shorter Channel crossing and a drive up through Germany and Jutland, and it was obviously slow compared with air services, so the emphasis was on marketing the crossing as a mini-cruise to start and/or end your holiday. It worked, because on a ship like the Anglia there was plenty to do - restaurants, bars, shops, cinema, conference rooms, disco, lounge with live band and dancefloor, big children's play area etc. It really was like a hotel at sea.
Of course, the North Sea can be rough - it was a chance you had to take - but I've been on the Regina in a Force 11 and it was great fun; I certainly never felt scared. The Brits stoically insisted on dancing the night away in the disco, every so often landing in a heap in one corner laughing madly! I never went on the Sirena Seaways (not to be confused with the earlier Dana Sirena that DFDS used, along with the Dana Corona, in the Med), but I'm told her seagoing qualities were dreadful. And maybe people have become more nervous these days and expect a natural element (the sea) to be like a motorway.
I agree that DFDS may have used the emissions rules as an excuse to close the route, which was probably losing a lot of money, but the criticisms are valid of excessive regulation produced by the EU's office-bound bureaucrats who know nothing about the shipping industry. Ships are far cleaner than road or air transport per ton-mile.
The closure is all the more unfortunate because DFDS was a leader in environment-friendly initiatives (one of the first to stop dumping ship's waste into the North Sea) and Scandinavia is at the forefront of clean-ship technology such as LNG power. Low-sulphur fuel is expensive and in some areas is hard to source. It can also cause mechanical problems, especially when ships have to switch from standard fuel to low-sulphur and back again, causing more wear on components and, potentially, more pollution! Scrubbers (which clean emissions) are expensive to fit and potentially reduce efficiency, resulting in more fuel-burn and hence more pollution. Now we have a situation where EU anti-pollution rules at sea will result in massively increased pollution in Europe's towns and villages from extra road traffic. Still, I dare say it all makes sense in Brussels!
The 1875 date for the opening of the route is slightly misleading, as this was the date DFDS began using Esbjerg. The UK port at this time was Thames Haven and North Sea services only switched to Harwich in 1880. The first passenger sailing was by the 835gt paddle steamer Riberhuus (imagine being in a Force 11 in that!), which left Esbjerg on 2 June 1880 and arrived at Harwich on 4 June. Parkeston Quay formally opened in 1883, I believe.