Playing an electronic organ, or even a pipe organ with electrically controlled action, in a moderately sized room, does not have these problems. So, why do so many hymns come out as funeral marches? The answer is, they don't, all. Sometimes, the organist plays too fast (I've seen it done, believe it or not).
I think the main problem is that any time one is playing a hymn that isn't part of one's own personal repertoire -- a hymn that one doesn't have a personal connection with -- and especially if it's one that the congregation isn't singing out strongly on (which is a lot of them), then one will tend to just feel one's way through, without any real sense of the dynamics of the hymn. The result is that sometimes fast hymns get played slow, and slow hymns get played fast. At my last appointment, we had one of the best organists I've ever had the pleasure of working with, but I could tell when there was a hymn she didn't know well. She would follow my voice, if she could, but if that wasn't possible, well -- suffice it to say that there were a few hymns I just quit picking.
And it's not just unfamiliarity with the tune, or even with the words we're singing. There are not a few hymns in the Hymnal that are written in straight notation, but which everybody sings in "swing time" or something. If you don't know that, and are just playing "book-value," then the hymn comes out lifeless. (Check out "My Hope is Built on Nothing Less" in the UM Hymnal. Nobody sings it like it's written there.)
Then, too, many organists play their instrument more or less like they play piano. But when you do that, the notes mush together. This can lead to the comic effect of "roller rink music" when they try to play hymns written specifically for the piano. But even in four-part hymn arrangements, piano technique will yield a lifeless result. In classical organ technique, one plays repeated notes staccato and moving notes legato, giving a distinct snap and crackle to a well-played tune on the organ. If you don't know that, and you're just trying not to sound awful, the easiest way to play is slow.
Meanwhile, there is the aggravating tendency among hymnal editors to change hymns originally written in 2/2 to 4/4. For some reason, a lot of musicians -- including well-trained ones who ought to know better -- have trouble playing hymns where the basic note is a minim rather than a crotchet: 2/2, 3/2, and (God help us) 4/2. But if you take a lively march written in 2/2 and play it, Sousa-style, in 4/4, it becomes (as one teenager said of one such as played by her grandmother) "the longest hymn I have ever sung."
In the end, there isn't any hard and fast rule about how fast to play or sing a hymn. Sometimes, the feel of the room will affect how one chooses to interpret a familiar song. And sometimes, you just want to get through it. When the Beatles were still touring, they got tired of doing concert after concert. If it wasn't fun with that audience that night, they'd just nod to Ringo, who would pick up the beat, and they'd finish the whole set quicker and be out the door. I've been in church services where I wanted to be able to do that. Haven't you?