I just did a test there and I could create a route on the fly on my android phone in Komoot and download the gpx.
Now, the quality of that route I'm not going to debate.
The relevant point though, is the practicality (or otherwise) of route creation on the road on a phone (or tablet).
The subscription apps (RWGPS, Strava) have varied their offerings over time.
Also, as you've pointed out, functionality varies from the Web to the app.
Then, there's the transfer (or not) to a gps unit if being used.
To anyone considering doing this on tour, I'd strongly suggest stress testing whatever options they choose in as real a scenario as possible. At the most basic level, route planning on the road is very, very different online and off. Using a touch screen in the rain is another!
Something I have often done is to create multiple versions of the same route as I tend to like to wander off course. If I find myself under pressure or on an uncomfortable route, I load up the one that is closest to me and follow that.
Cycle.travel has worked for me countless times on the road (Internet permitting) and yes, it's not the most phone friendly but I do trust its routes (which to me is the most important). The good news is that app versions are on the way, although Apple will be first.