Buying train tickets online

No reason at all. Trainline is often recommended by people on this forum as an alternative to the individual national rail websites ( which in some cases are tricky with US credit cards).

It is Rail Europe that draws the criticism, because they do not show complete schedules, and they do mark up the prices.

We used https://www.trainline.eu/ successfully for our France trip a couple of years ago and found the site much more user friendly than SNCF. We have the trainline App on our cell phones and use e-tickets.

That said, in Italy last year we only used regional trains so there was no reason to buy tickets in advance. Also, in Switzerland https://www.sbb.ch/en/leisure-holidays/travel-in-switzerland/international-guests.html offers various discount passes and cards that may be beneficial for your trip.

It is currently the best site most user and price friendly for booking tickets for multiple national rail lines. But I only see a need to use it for France and Spain as all the other national rail sites are pretty easy to use and they send me deals. I don't receive deal alerts from trainline

is there any reason why should NOT buy our tickets through this site

NEVER buy regional tickets online from Trainline (or from the Bahn, or from anyone else, for that matter, particularly RailEurope). Buy them at the station just before travel. Both Trainline and Bahn regional tickets are subject to a penalty fee if exchanged/cancelled on the day of validity. If you are late to the station, sorry. If you change your mind and want to travel earlier or later, sorry.

So far I can't find any problem with buying tickets for travel on long-distance trains from Trainline, but there is no advantage either, and for planning purposes, Trainline is still not very good.

Germany has a lot of rail stations, over 5000. A lot of towns have stations, but those that don't usually have some kind of bus service. The Bahn website shows buses, Trainline does not.

If you go to Trainline and tell it you want to go from Oberammergau to the castle bus stop at Hohenschwangau, it won't recognize Hohenschwangau, at all. All it will show you is a four hour train connection through Munich to Füssen. The Bahn, on the other hand, shows you a 1h20 bus connection leaving Oberammergau at 8:30, arriving at Hohenschwangau at 9:50, as well as three other connections throughout the morning.

The Bahn has about 1000 train stations in Bavaria; RVO-Bus alone has over 10,000 bus stops in southern Bavaria. I've never found a town in Bavaria I could not get to by bus if not by train.

The Bahn won't show the bus fares, but they will be quite nominal. An all-day pass (Tagesticket) for unlimited trips on RVO buses in a day is only 10,20€/adult, and if you are already traveling with a Bayern-Ticket, the RVO buses are, in most cases, included. Excluded buses are mostly special buses, like the buses up to the Eagles Nest, buses on toll roads, and buses traveling outside Germany, like RVO 840 from Berchtesgaden to Salzburg.

If you happen to be familiar with the local metro transit districts (Verkehrverbünde) in Germany, you can also find lower fares (ex. FRA to Bacharach is 12,20€/P with a puchase-at-the-time RMV (Frankfurt metro) ticket vs. ~19,-€ and up for an advanced purchase ticket with limited exchangeability from Trainline.

Is there any advantage (cost or availability) to purchasing a regional train ticket, e.g. London to Bath, online prior to arrival in London?

For a one-way ticket? Probably just as expensive.

London to Bath is long-distance, not regional. If you can book more than a couple of weeks in advance you will almost certainly save a lot of money.

For London to Bath, Philip is right and Continental is wrong.

On trainline.eu, be careful about using it for tickets in Switzerland. I just priced a sample journey (Zurich to Luzern on Friday 25 May. On the SBB site, the standard price is CHF 26.00, and supersaver tickets are available for as little as CHF 7.80. On trainline.eu, it's quoting me a price of 25.80 euros, or CHF 30.86, and supersaver tickets appear not to be available.

You might be able to save a few Euro by booking your train tickets online in advance on each of the countries' national rail website. But you'll need to factor in the aggravation factor of dealing with some of those websites which can be problematic sometimes. So yes, I would buy from trainline.eu if you can get them all at a very good price.

For London to Bath, Philip is right and Continental is wrong.

Wow....yes I am! Last night, it showed the same exorbitant three figure price on Trainline or at least that's what I saw in the middle of the night. Just now I went to the National Rail journey planner (much better than Trainline as I learned from this forum as Trainline is a 3rd party booking agent that charges a fee) and see there is a cost savings from advanced ticketing on that route. I found a £15 one way in 90 days. That's AWESOME.

"My question is, is there any reason why should NOT buy our tickets through this site?"

No reason at all! Trainline is the site I use most often for buying advance tickets in Europe. They don't currently sell tickets for all rail networks in Europe, but they're adding more all the time. Once registered on their website (with payment information), the process is very easy.

If you haven't travelled in Europe before, note that you'll have compulsory seat reservations on the express trains in Italy, and also on the TGV in France (those will be included with the tickets).