I've climbed it twice - once in the late 80s and again early 90s. The first time, I spent the very uncomfortable night actually on the mountain itself though very little sleep was had on a thin mat and sleeping bag atop uneven stones. However, that night was one of my lifetime 'wow' memories with a magical sky - completely unaffected by any light pollution at all - the likes of which I've not seen since which was awash with stars of different sizes and brightness, many many shooting stars and the clear repetitive tracks of satellites. It was an amazing 'show' and I was in awe of nature. As a naiive young 20 something I climbed with a large rucksack, wearing moccasins of all things. Doing that now would terrify me, how I didn't slip and injure myself I don't know.
I remember a little old man at some point near the summit who was selling tea and hot chocolate to the climbers and appreciating how it was piping hot in the freezing night air.
Second time round - in walking boots this time - I set off at 2am in order to see the sunrise. It was even colder then (December vs September) and I recall being so bitterly cold that I really struggled to get my lenses in as I was shivering so much. My group was staying in a very basic hostel within walking distance of the mountain's base ... beds on concrete platforms, rough wooden doors. This added to the middle of nowhere 'otherness' of the whole experience. Climbing in the gradually dawning morning light I remember how colourful the stone ridges seemed ... shades of purple, red and orange.
I also visited St Katherine's monastery ... like you, I'm not at all religious but you would have had to have a very hard heart not to respect the feeling of dedicated spirituality which the monastery seemed to have. I remember being fascinated by the ossuary there; I'd never seen anything like it but it wasn't frightening, and seemed a practical and respectful solution to the difficulty of otherwise maintaining a graveyard there for the monks. My dad had visited St Katherine's 40 years before I did during his national service so I also felt a connection to him in this very isolated location. At that time, people, animals and goods apparently entered the monastery via a large basket which was hauled up the wall to a high entry point.
Like you, I definitely felt very moved by my visits, particularly the first, because it was such a shock to the system (in a good way). And regardless of my lack of faith I was also very conscious of how important the site was to the 3 major religions. Even being young I very much felt a sense of privilege to be there and see something so important and so remote. To get there each time had taken a very long, bumpy and dusty drive across the desert.
I hadn't known anything of the area being developed at all so thank you for linking to that news item. It's a big shame in my opinion as easier access from the Red Sea resorts will inevitably turn it into nothing more than 'something to do' for some people who may not be aware of, or care to find out about, its history and significance and as with many popular tourist 'attractions' you then run the risk of a lack of respect being shown. When you've got to your destination by a somewhat arduous journey, you're more likely to genuinely want to go there for the sense of achievement / history / appreciation of the natural surroundings and / or the religious significance.
I wonder if, with the government pushing ahead, whether the monastery will be able to retain its automony and restrict visitor numbers to a level it feels comfortable with? It is, after all, a place of both work and worship. As for running a cable car up the mountain itself ... well, that's really quite upsetting to be honest though I have no right to feel like that personally of course. It just seems so incongruous and disrespectful, again, given Mt Sinai's to believers.
I don't think I'd want to go back again now or in the future and would prefer to see it in my mind's eye as it was.