There are two principal reasons that big tech pulled the Parler app:
1) As a basic matter of contract law the platforms reserve the right to cease hosting an application without notice or cause. Here is a sample from the Amazon App store's Term and Conditions (This is from the consumer side because I couldn't find the developer side quickly),
"3.4 Compliance with Law and Reservation of Rights.
You will use Apps in compliance with all applicable laws, including all export and re-export restrictions and regulations of the Department of Commerce and other United States agencies and authorities that may apply to any App. We reserve the right to change, remove, suspend, or disable any App without notice or liability."
This is pretty standard stuff which includes the terms and conditions of this particular platform here at Trioandfriends which reads:
By accessing “Trio and Friends” (hereinafter “we”, “us”, “our”, “Trio and Friends”, “
http://trioandfriends.com”), you agree to be legally bound by the following terms. If you do not agree to be legally bound by all of the following terms then please do not access and/or use “Trio and Friends”. We may change these at any time and we’ll do our utmost in informing you, though it would be prudent to review this regularly yourself as your continued usage of “Trio and Friends” after changes mean you agree to be legally bound by these terms as they are updated and/or amended [...] You agree not to post any abusive, obscene, vulgar, slanderous, hateful, threatening, sexually-orientated or any other material that may violate any laws be it of your country, the country where “Trio and Friends” is hosted or International Law. Doing so may lead to you being immediately and permanently banned, with notification of your Internet Service Provider if deemed required by us."
The fact of the matter is that there is a contractual obligation upon both the developers and the users of programs to follow all applicable laws. In the case of Parler, the evidence suggests, particularly regarding the capital event, that the application was being used to orchestrate and enact illegal activities, and thus big tech was justified in wielding its contractual rights to suspend support for the program.
2) Technology law is rapidly evolving and while for the time being, big tech has managed to reserve immunity for itself from liability for most of the content that occurs on the platforms that is not likely to remain the case. For example, Facebook is not currently liable for defamation that is posted on its site despite the fact that a newspaper is definitely liable for defamation that is published on its pages. So big tech has managed to find this sweet spot of operating, where it gets to wield editorial power over content (via contract law) without the liability exposure of editorial responsibility that other media companies bear.
It is undeniably within the interest of big tech to keep this arrangement. (that's one of the reasons they put the illegal activity clauses in their terms and conditions) But, politically they must be cautious. If they find themselves on the wrong side of the political tides they will lose this liability protection and find themselves complicit in criminal behavior. In the end, they will lose money and incur great risk. Thus, there are business interests in play to make sure they at least make an appearance of being good citizens in the community.