Why do Jews who go to Beis Din to resolve a financial disagreement, often use "lawyers" (to'ein) to argue their respective sides. If the dayanim are capable shouldn't they be able to just heard the sides and make a decision based on the Torah? Also, doesn't this lead to the richer side being able to hire the better "to'ein" which makes it unfair?
You happen to have a very good point,in fact the Shulchan Aruch CM 13:3 and the Sma 12 write that the dayanim should really only hear from the person himself and not from a toein.
In this article Rav Hershel Schacter explains in detail how corrupt the toein system is and how people are making a fortune off this "profession ".
The point is that the individuals are often too nervous to actually show the facts of the case. Also, they are afraid that if the dayanim are not given all the arguments by their side, that they will not get a fair hearing. Part of this is the influence of the American court system. The dayanim are expected to be able to discount the to'ein when necessary.
After much criticism of my first answer (fairly so), there has been much more research and neutralization of the source. To be clear, my first answer was not promoting any program. I was trying to fairly give the source's context, which might be skewed towards the use of To'anim in a Bais Din. (To keep this answer neutral, you can look into the source about to be quoted yourself by searching what Rabbi Meir Simcha Lerner does in Lakewood). Still, Rabbi Lerner provides a rational Halachic source for To'anim as follows:
"The Halacha states in Shulchan Aruch Choshen Mishpat (Siman 17, Seif 9), "If a Dayan sees that a litigant is struggling to explain their arguments in an important matter, then it is permissible to assist him in formulating his argument as the posuk in Mishlei (31:8) 'P'sach picha l'elaim' or 'you should open your mouth on behalf of the mute' as long as you are careful not to be k'orchei hadayanim." This [has been learned to] mean(s) the Dayan cannot become the litigant's advocate. It is clear from this halacha that a Dayan can accommodate litigants stating their case, but the Dayan needs to maintain an open mind for all sides in the case.
The Gemora in Bava Kama 117b tells the story of Rav Abba, who incurred damage and was advised to go to a certain Bais Din that was known to rule in favor of people who incurred such damages. Rav Abba followed the advice and was successful in his Din Torah. [Also,] (a)s mentioned in Tosfos, Shavuos 31A, the Torah considers it a great mitzvah to help a person retrieve money or settle financial matters [and disputes].
Evidence of using the term To'en is found in [Shu"t] responsa from the 15th Century and on. There is also a teshuva in the 1400s from Rabbi Yisroel Bruna, an Ashkenazi Rav who was a primary source for the Rama, discussing the question of whether a To'en can switch sides in the case [proving that To'anim have been used in Bais Din for years]. The S"MA, Rabbi Yehoshua Falk, a talmid of the Rama, at the turn of the 17th Century, wrote in his Sefer on the Shulchan Aruch that it is already an accepted practice to have [one's] (your) case presented by an advocate [to'en] and there can be no objection to this. It is also known that To'anim were frequently present in the Bais Din of the Ha'fla-ah, Rabbi Pinchus Ha[L]evi Horowitz in the 1700s."
It seems that Rabbi Lerner disproves the common notion that the use of To'anim in a Bais Din was influenced by the American court system's use of lawyers. His multiple sources of To'anim being used in Eastern Europe before America was even a country is apparent and follows through in the quoted texts (not found online, you're welcome to search your local Bais Medrash).
Regarding the fairness of the Bais Din system works in our times, there are many issues with both the Dayanim and the To'anim based on Ami Magazine's article interviewing Dayan Schachter from 2011. I am not sure one can confidently say that the system has been improved since 2011.
Some of the noted issues with To'anim, as you ask and mentioned by Dayan Schacter, is that they're known to act very similar to the aggressive manner of lawyers in America's secular courts, where they obstruct litigants from answering questions directly asked by the Dayanim, and ultimately obstruct Yosher (justice).
In Eretz Yisrael, there is a more formal Bais Din system that is part of the justice system. Although it has its wide criticism for fairness and Yosher (justice) similar to the criticisms of the private Baisei Dinim in America, at least the system does have a more formal structure to qualify To'anim, including a required license to be a To'en Rabbani. The licensure is contrary to how anybody can be a To'en in America, although we often find that they're usually lawyers and sometimes also Rabbis.
The biggest issue is the general concept from Avot (1:8) "אל תעש עצמך כעורכי הדיינים" which literally is telling the Dayanim not to act as lawyers for their litigants, as was mentioned by the quote from Rabbi Lerner, above. Although it doesn't mean that it excludes To'anim's ability for representing litigants (as contrarily, one can argue that the Mishna is a source in itself for the To'anim system.) Still, the Mishna's clear instruction to Dayanim is an issue we see with the Borerim system.
In the Borerim system, a Bais Din is formed by each litigant selecting their Dayan and the two Dayanim select a third Dayan. It's often considered straight shochad (bribery) in many talmidei chachamim's opinions because each litigant has to pay their Dayan for one-on-one sessions (where Dayanim often guide the litigants like lawyers/To'anim). Litigants then also pay for the Dayanim's time in Bais Din, where often the litigant who paid their Dayan the most usually wins the Din Torah, according to Dayan Schachter.
Your question is valid where money is often the major factor, and the litigant that pays most often gets his/her way.