Competition is great, in theory, except that when you have many companies that can compete with each other - they end up buying each other, or forming cartels to control the industry.
You then need a regulator with strong teeth.
Besides, it doesn't work on a single route because of path-blocking and lack of flexibility to alter timetables. Given two routes between the same basic points (Paddington-Exeter and Waterloo-Exeter for instance) than the operators (FGW and SWT) can compete effectively. Or at least they could if SWT could make decisions about investment in the route, such as full dualling and speed increases - remembering that their fastest service is still slower than the
ACE in steam days. That can't happen under the current model, indeed timetable changes have to go through a different authority. The GWR and SR were effective competitors on London-Exeter, FGW and SWT are not.
As for cartels and mergers, they were very much the thing in the pre-grouping. The "Euston Square Confederacy" operated for years, involving the LNWR, the Midland and the MS&LR with an effort to stop the expansion of the GNR, principally aimed at stifling GNR London traffic. It failed, leading to the Midland deciding to build its own line to London. Price wars were common, which was ultimately good for passengers but not for profits. Races developed to various places (London-Scotland, Plymouth-London, Dover-London and so on). Another cartel was the "Three Greats", GNR, GER and GCR. This was more an agreement to share traffic and not compete too much, and ultimately all three merged to form the southern LNER anyway.
All good clean fun, and ultimately of some benefit to the passenger and goods customer. Each company competed to build better, faster and more powerful engines, smoother, more comfortable and better appointed coaches and bigger, faster wagons. They owned the works that built them, so it was easy to do. New routes and new yards appeared regularly to tap new freight flows, while improved stations provided better passenger facilities. Basically, being an integrated company led to flexibility, thus improving competition. As for regulation, this was the Victorian era and it was minimal to say the least. Did that cause problems? Sometimes. Did it ultimately lead to a worse situation? In my opinion,
NO!
These unregulated companies were usually fiercely independent and protective of their territory. Look at the Hull and Barnsley railway, built to undercut the North Eastern and their traffic from Hull docks by connecting them to the GNR, Midland, L&Y and MS&LR. This provoked a huge price war, but did not put the H&B out of business, indeed Hull gained more traffic. If either had reduced service, the other would have jumped in and grabbed the business. Ultimately, they sorted out their differences, cooperated to build the King George Dock, and finally merged in 1921.
As for Mergers, the LNWR decided to acquire the L&Y to reduce competition in their home territory and intrude into Midland and GNR territory. That was more a political move than anything. The Midland bought the LT&SR to gain access to Tilbury docks, making this a strategic move. The SER and LC&DR merged simply because they had been competing for so long for the same traffic that both sides were really getting nowhere, and merger would be easier on both. If it were not for the Grouping, then the southern half of the LNER would probably have formed anyway (see "Three Greats" above).
OK, it might have been messy sometimes, but it gave us a network of track that very few countries match. On the whole, it was a good thing. Stifling it by splitting the wheel from the rail was insane, and I have no idea why anyone would think that it was a good idea in the first place.