From an SEO perspective. Google has stated, not all pages are worth indexing, Google specifically states they by design do not index the majority of pages they know about, which is in the trillions.
Duplicate content is a problem.
https://example.com/search/61-205/2023-12-28/
https://example.com/search/61-205/2023-12-29/
https://example.com/search/61-205/2023-12-30/
Unless these are significantly different. Search Engines would only have an interest in indexing one of them. Determining which one is the best one to index is also a problem, even if queries are used.
https://example.com/search/61-205/?date=20231228
https://example.com/search/61-205/?date=20231229
Many e-commerce sites are now having problems because Google removed the option from Google search console, to tell Google not to index the query strings.
This is related webmaster Question but is not specific to the console
change.
How to keep crawler robots from indexing my page when there is a query string present in the URL?
When search engines are willing to index one of many duplicates the problem becomes which page. If the page keeps changing, and with a schedule, it would, the page, which is indexed, never matures and never gets the benefits from Google's algos related to interactions.
Adding another level does not fix the duplicate problem
https://example.com/search/61-205/2023-12-28/stationA-to-stationC
https://example.com/search/61-205/2023-12-28/stationA-to-stationB
What is the difference between these pages? Having the page title, heading, and one line of text be different is a duplicate in the eyes of search engines.
https://example.com/search/61-205/2023-12-28/stationA-to-stationC
https://example.com/search/61-205/2023-12-29/stationA-to-stationC
Are also duplicates in the eyes of search engines as only the date has been changed.
Possible Solution
https://example.com/schedule/61-205/
Can be the indexable page for the train 61-205. Schedule can be used in the URL as it is a possible user query keyword and having it in the URL is helpful for SEO.
https://example.com/schedule/61-205/itinerary?date=&station1=&station2=
Can be the fixed URL that people can share. But make the itinerary page no index; As it will be duplicate content for SEO.
Disallow: /schedule/61-205/itinerary?
https://example.com/stations/StationA
Would also be useful SEO fodder as they are all unique and people may search for them.
https://example.com/stations/StationA/61-205
https://example.com/trains/61-205
May be useful if there is enough information that is different between trains. They would also be useful to have the get a Quotation Search on which leads to https://example.com/schedule/61-205/itinerary?date=&station1=&station2= which people can share, email, etc.
On additional consideration on SEO Structure
A structure of
https://www.example.com/trains/61-205
Page tells people about the train.
https://www.example.com/trains/51-205/schedule/
Provides gain of information about the schedule and stations. Maybe some specific points of interest or places for photography. The provided schedule would be for today ... with the option to search for a different date.
https://www.example.com/station/StationA/
provides information about the station.
https://www.example.com/station/StationA/schedule/
Provides gain of information as to which trains are coming and going and destinations of interest. The provided schedule would be today. With box to search on another day.
https://www.example.com/itinerary/
Would be the search or quotation portal.
https://www.example.com/itinerary/results
would be the user-sharedable links, which would have the duplicate problem for SEO so they are no-index.
For additional fodder.
https://www.example.com/holidays
https://www.example.com/points-of-interest
https://www.example.com/photographers
https://www.example.com/photographers/shared-photos/
https://www.example.com/discounts
https://www.example.com/specials
The SEO fodder list goes on and on.