Without having a home field/being at a home field, a team does not have emotional support or field familiarity that will make them more comfortable to do their thing on the field. To any individual or team, morale greatly increases being home, and this can make a big difference. There are many articles and athletes that can provide this as well.
Just like in any scenario, (well in some scenarios) when you are at home, you feel comfortable, you feel supported and as a result emotionally and mentally in a good space. This idea is could not be more prevalent than in professional sports. When a team place at home, they are completely familiar with their surroundings, they have more fans to support them and cheer them on. Such factors definitely make a difference in a team’s performance.
I think it really depends on the team. I have seen some teams where home field advantage is the difference between winning and losing but there are some teams where that difference does not matter, and they can win no matter where they are at. In most circumstances, yes, it works to say it.
Of course home field advantage makes a difference. If you look at the numbers you will see that home teams win more than road teams. That stat goes across all sports. Having the home fans behind the team definitely helps a lot. Players feel comfortable at home and play better.
In just about every sport, all you have to do is look at the statistics of homes games compared to away games. There may be occasional exceptions, but they prove the rule that teams nearly always do better at home. They benefit from the crowd, they know the intimate details of the venue, and they simply have more practice in the setting.