This is a good topic. I have an opinion and can share some past experience. I will state upfront that I do not believe there is a perfect answer. The above mentioned reasoning by so many is proof that situations require different mindsets to decide what is best.
Coaches want larger rosters to give them more options for each individual situation that can present itself per game------perhaps per inning. We have the luxury of being able to re-enter players which in turn helps us most of the time. Having the opportunity to "play" more than 9 players by utilizing the roster format is a big help. Many coaches struggle to understand this system including me, but it is there.
Players want to play. Doing anything is still better than nothing but ultimately their goal is to be active all the time. They struggle to be delegated to being a FLEX or DH because they don't consider it a primary position. Players want to be top 9. In those top 9 they want to be in the first 4-5 spots in the batting order. It's the competitive nature of a human being to be "King of the Hill" and to be dethroned can be a negative emotional experience.
While many good coaches take time to explain so many facets of the game, they ignore the impact of something as crucial as the batting order. It's put together by coaches for all the right reasons. They simply don't convey this to the players or more importantly to the family that can judge you. Many coaches leave this detail with a "Because I said so" attitude and that can come back to bite them in the butt.
Having said this, how do you decide how many players you should carry but more importantly how are you going to use them?
Travel rosters are going to be different from REC or school ball rosters. Let's talk travel ball. The first mistake a travel ball coach can make is to carry a larger roster simply to get money (fees). Do not carry a player if there is no intent to play the kid. If a parent insists their child be a part of the team you need to be perfectly clear their involvement would be for the experience and social aspect only. There would be no expectations of ever taking the field. Yes, this does happen. Coaches, make the parents sign a contract to have this documented. They hope by socializing they can somehow crack the ranks and get their kid in the rotation. Don't fall for this ploy.
Parents expect something for their investment (fees). Do not blow them off with the practice and experience is what they are paying for. That's a smoke screen they will eventually see thru and become a real problem later. If you need more money to have the season you want, raise your fees or do fundraisers. Anything else is unethical.
With a mindset that you need to play the girls most if not all the time, how can you achieve this? Diversify the roster. Plan on having pitchers playing secondary positions when not pitching. Have an extra catcher or 2 that can play other positions. They can't all pitch. It's unreasonable to expect 1 catcher can always catch every game. Develop the skills of others to be ready to go whatever might happen. One foul ball to a catcher and you may lose her for a weekend. One line drive to a pitcher and you could lose her as well. This, in a nutshell, is how a coach needs to plan a roster selection to insure the best result you can have under extreme circumstances.
It's been my experience that new teams will probably lose more games than they win. Normally that means playing the minimum amount a games guaranteed on any given weekend. With this, you may not get into a scenario where you need such diversity unless there are injuries or girls not coming. The same can be said for elite teams that just win, win, win. They play the minimum amount of games needed to win it all. It's the teams in the middle. Those teams that may get put into the loser's bracket early, yet make a strong run till the end that really test the fortitude of your roster. All you can do is make the best of it and take the result. You cannot structure a travel ball roster for those moments.
One of the "gimmicks" I used to implement was what I referred to as my "A" list of players. We live in a rural area and fielding a complete roster of dedicated girls for an entire season, without distraction, is not going to happen. The kids are involved in 4-H and FFA, they attend camps for basketball and volleyball that are "voluntary" by the school coaches but can't miss. Most are 2-3 sport athletes, even at 10u-12u age. Because of this, there will be weekends where subs are needed for the team to compete. I would select a core roster of 11-12 players. Others with potential will be offered a chance to be on our "A" list. They signed a contract for being on this list. They did not "pay to play". They were welcome to attend practices with the team and treated mostly equal in receiving instruction from staff. They did not get the perks (uniforms and such) but for the most part were handled just like roster players. If they wanted to come to the games they were welcome to come and sit the bench with the regular players. Their names would be on the tournament roster. They could purchase their own uniform to wear if they wanted but at no time were they considered for any playing time.
Here's the kicker, in the event that our roster was compromised, we would put them in. If we had a player/players that told us they would not be able to play a weekend due to another activity, we would call an "A" list girl up and activate her to full roster status for the day/weekend. If called up, she would receive the same treatment as a full roster girl and get her share of the playing time that predetermined time frame. We had spare uniforms available for her/them if needed but they had to turn them back in after the last game. If our regular girl showed because their activity was canceled or finished early, she sat the bench like an "A" list girl during that time frame. I am not going to go thru the pains of asking a girl to sub, then sit her just because a regular changed her mind or her other plans fell thru. I don't care if she's my starting pitcher---------she sits. Again, it's only ethical.
This "A" list concept achieved a lot of goals. It gives a coach a running list of reserve players to call upon. They practice with the team so they know the system and the staff. It gives us as coaches the opportunity to extend our instruction to more girls to help them hone their skills. Ultimately, coaches are teachers and should be teaching and mentoring. No dropping out of tourneys or forfeits due to player issues. You would be surprised how many girls/families would take advantage of the opportunity. It works!
To me, it is a "win win" for everyone while remaining loyal to your regular roster and remaining ethical.
To summarize; carry a tighter roster and be willing to play with as few as 9 in any given game but with the "A" list working you can do it knowing your back up players are standing by without expectations.
