Without delving too far into “why” (or rather: not at all), I’d like to pick everyone’s brain about all the things that make the difference between a LH-style network carrier and an FR-style LCC. I have a few important ones on my list, but I want to find out what I might have missed.
So…go! 
Ryanair…
BA
Biggest difference to me is how the demand is addressed:
They understood that offering a service might actually create the demand the service fulfils.
Just some quick thoughts on additional differences:
LCCs usually use airports with lower landing fees or LCC terminals to lower their cost. They also take advantage of P2P demand (and passengers willing to travel more distance to the airport in order to save on the ticket price) while legacy carriers are more or less hub-based.
They also try to reduce the turnaround time such as using duel door boarding etc, and also more plane utilisation over the days.
A lot of LCCs also have hidden fees, such as airport check-in and carry-on baggage fees; I think Ryanair even has credit card fees. I think one way to explain it is they will attract passengers with the lower starting ticket prices, but it is the passengers’ responsibility to keep it that way.
There are also obvious seat size differences as LCC basically pack as many passengers on the plane as possible.
I think also need to mention that some of the LCC carriers are not really low-cost at all… I think southwest and jetblue in US are pretty good examples… their ticket prices are not actually much cheaper than the legacy carriers… so some parts, e.g., boarding and turnaround time, are not really keeping the LCCs and legacy carriers differ, it is probably more on operational cost-cutting in general.
I think some other differences could include:
Much less, or almost no, reliance on connections, externally (such as ILs/etc) and internally (though programmes such as Lion Connect and the new Ryanair scheme are beginning to grow in importance). Networks are beginning to grow as the saturation for small bases becomes apparent in the last decade or so. the big 3 LCCs in EU are condensing bases especially post-pandemic
The time of booking: for many airlines in the network carrier a decent chunk books last minute, whereas usually people plan out in advance even Ryanair vacation schemes (for example in the US the Southwest next release-flights-for-pax-booking day is always anticipated). Though with the low cost carrier the payment doesn’t all come at time of booking, usually.
Another one I noticed recently is the number of inventory (booking) classes: whereas with ntwk carriers you have almost an A through a Z, WN and G4, among others, only have one inventory class these days. I know WN didn’t use to be like this…
Times of travel: the network carrier seems to tolerate much less bad flight timing, except in the case where the grand majority connect (looking at you, 2 AM EY wave in Abu Dhabi)
Many LCCs are ticketless airlines
and I’ll edit when I think of more 
In Canada we have had fewer LCC options until recently. What I have noted from them is many of the items noted above:
Btw i got some of these fees from a current LCC that is flying in Canada from their website. Some of them even surprised me like the overhead cabin guarantee fee. In addition some of the extra fees were based on distance traveled - so extra leg room seats cost more to book ahead if you were going 2500 km vs 1000 km.
Cheers,
Regan
Another important one:
LCC, especially ULCC, tend to have disproportionally more non-daily flights than network carriers. ULCC have flights that range from 1 to 7 days per week, but most flights on thin city pairs is 2-3 weekly flights.
ULCCs also tend to fly the route at different time of day on different days. This is due to increased aircraft utilization and scheduling. But you barely find the Monday, Wednesday and Saturday flights to depart on the same hour, sometimes it’s just few minutes difference (10.10 vs 10.30 am) and sometimes it’s several hours difference (10.20 am vs 2.40 pm).
Also, LCCs and especially ULCCs tend to have much more late night or very early morning departing flights compared to network carriers. 1 am departures are nothing unheard of, as well as 4 am departures (though for AS purposes this would be moot point).
That is not only limited to LCCs and ULCCs. Watch BOM for example or DXB. You will find also premium carrier departing all night.
One item that hasn’t been mentioned yet. I believe network carriers employ their own staff, which is often unionized and have lot’s of perks, seniority rules and social security covers. Staff has monthly salaries, with part of the salary paid on hours flown.
Ryanair (and presumably others) outsource their crew, consider them self-employed. Staff is purely paid on hours flown (sometimes it seems not even block time) and social security costs, paid vacation etc. is the responsibility of the employee.
I also believe legacy carriers have their own flight schools and career programs, training pilots by using them as second (or third) officers, while ULCCs only hire pilots with an existing license. Education is their own responsibility.
ULCCs keep all their (admin) costs low, by having offices in containers in cheap locations, ask their staff to bring their own stationary etc. Legacy carriers are close of airports and need prestige locations for their offices.