Privitisation has made fares far cheaper if you know what you're doing, it's great for people with a hacking mindset who aren't worried about looking at brfares.com, and maybe investigating things like routing guides.
Advanced fares exist to encourage people to travel by train who wouldn't normally. They are released on trains that are generally more lightly to get more revenue from perishable stock. Same as supermarkets selling lunch food near expiry date cheaply in the evening - they don't want to do it earlier in the day (and canibalise their lunch trade), but doing it at 4pm means they get extra money without revenue abstraction.
I'm not a fan of advanced fares though, I don't tend to plan, and I hate the stress of missing the train, so I look for hacks to get better flexible fares.
A Manchester-London "standard fare" has increase from £50 in 1995 (£100 today) to £160, however competition and sties like trainsplit mean you can buy a walk up return fare for £45 -- less than a quarter of the old cost after inflation, and only about 20 minutes longer than the old time.
There's more "hacks" to be had too. I used to travel from Wilmslow to London on a semi-regular basis (every few months, getting the 0811 fast train, and returning about 6pm. It cost about £120 return, because I bought a super off peak ticket from Edinburgh, which was valid on any train arriving into Euston that was on the route. Break of journey is well worthwhile - I travelled from Crewe to London a fair bit on a Chirk-Tunbridge Wells return, which allowed break of journey in both directions and was valid on so called "peak" trains from Crewe to London. Splitting tickets can work, especially on very overcrowded trains like the cross country services. Don't buy a pricey ticket from Exeter to Leeds, instead buy a combination of tickets for your journey and save a fortune.
All this means if you are willing to put in time or effort you can travel far more cheaply. The goal of the "rail delivery group" over the last few years has been to remove these "hacks", so everyone has to pay the full price.
Other options to reduce fares would be
1) Getting rid of the unions (rail staff have a strong contract meaning driver salaries have increased about 5.5% a year since privitisation -- same as the "standard" fare on the Manchester-London ticket)
2) Reducing staff (DOO where the driver has to press the "door open" button instead of the guard. This led to massive industrial action on both Northern and Southern)
3) Increasing train speeds (A London-Manchester return takes about 5 hours for staff, costing 5x3 salaries for the driver, guard, and buffet. Replace with HS2 and it drops to 2.5 hour round trip, halving staffing costs - and train leasing costs - and the HS2 trains are twice the size so there's twice as many seats so no need to price people off "overcrowded peak trains")
4) Increasing taxpayer subsidy. Given that the majority of rail travellers are of an above average income, and especially on the really expensive lines
The left have painted a picture of Richard Branson having stolen trillions of pounds over the years, but the profit margins are really very small. It might account for £5 on that £160 ticket, but that's not going to make people happy. I'd rather have the option to learn how to get cheaper tickets (typically typing in "trainsplit.com"). Sadly the narrative (see many posts on this thread) is that "privitisation means high fares and poor service". The evidence is that is nowhere near the whole story. Well respected rail journalist Mark Smith does a good balanced report comparing fares in europe and UK, and the reply comes "load of rubbish guvnor, check the prices now". I check the prices now, post screenshots which back up Mark Smith's points, and it's just a downvote with no reply.
I thought HN was a rational place, but it seems not when it comes to the UK railway.