Seems logical right? No more soviets to fight, it kind of lost it's purpose then.
For a more abstracted and theoretical answer, I would recommend reading James March and Johan Olsen's article "The Institutional Dynamics of International Political Order".
Essentially, they argue that international institutions, such as NATO, tend to stick around because history is not an efficient process. In other words, actors and institutions do not come into existence to solve specific problems and then cease to exist once those problems are solved. Such a view sees institutions simply as a product of a changing environment. March and Olsen argue that institutions also shape their environment once they are created. Problems are now defined in relation to the existing institution, actors get comfortable acting within the institution, and the bureaucracy of the institution itself want to preserve it in order to protect their livelihood. All of this adds up to there being too many short term costs to abandon an institution and learn how to operate within another when you could just adapt the institution you already have.
So to apply this theory to NATO, the NATO members would have gotten used to cooperating within NATO and viewing problems in relation to NATO, while the bureaucracy would have worked to alter NATO's identity and capabilities in order to make sure it remains relevant. Thus, NATO has shaped the way its members think about the world to an extent that it is easier to operate within NATO than to abandon it.
I wrote an essay on exactly this for university last year, so I'll copy over the substantive part of it here for you. The short answer is that NATO's purpose has fundamentally shifted, and it provides benefits to all of its members that exceed the potential benefits (if any) of dissolving it.You need some historic context as to why NATO existed: it's a bit more complex than just 'because Russia', and in some ways arises out of preexisting European security arrangements and a serious concern that even united Europe couldn't stand as a front against Russia. The United States was less than okay with this, particularly due to shared history and values (but also to a great level the economic importance of Europe as their largest set of trading partners at the time), and was aware that a war with Russia wasn't just a physical one, but a war of ideology and image as well, and the west needed to look strong and capable to survive. There was also an awareness that the UN Framework didn't facilitate this.
There's a publication by Wallace Thies called "Why NATO Endures" that might be of use; it's published by Cambridge University press.
NATO was created in order to defend against external threats. However, if this was the only reason for its existence then it should have ceased to exist at the end of the Cold War. NATO has continued to exist because its role has changed: it has shifted to new areas of international security, taking a more proactive role in combatting threats. Further, by virtue of being comprised of liberal democratic states and being a democratic alliance, NATO has inherent structural safeguards that have ensured its survival.
NATO no longer acts as a purely defensive body. It has undertaken a number of proactive campaigns. From 1992 onwards a NATO intervention force existed in Bosnia, and in 1995 this expanded to include ground troops. In 1998 NATO intervened in the Kosovo crisis with an extensive bombing campaign, saying the intent was to avert a humanitarian catastrophe. In 2001, NATO treated the September 11th attacks as an attack on all members, and this resulted in their involvement in Afghanistan. This involvement was a frontline role and attempted to directly combat terror groups, making it a departure from NATO’s traditional defensive role. It can also be seen in Libya: intervention was permitted by the Security Council, but NATO was the only international organisation that undertook military action. Others, including the African Union, preferred diplomatic dialogue. Besides this, NATO has also begun to undertake operations such as airlifting supplies to disaster zones which are not strictly in its original mandate.
These examples show us that NATO and its members have a shifting role in the international system. The organisation has taken on a more proactive and intervention-based role, meaning it is more than just “collective defence”. It has been argued that intervention in Kosovo and Bosnia reflected a change in foreign policy for European members: they had an idea of a “European project”, and eastern European states were a part of this so had to be included. It could also be a result of a unipolar world: with the United States as the only real world power, it could use NATO to intervene in areas outside its typical sphere of influence, but in ways that benefit its national security and maintain its hegemonic status.
NATO has certainly shifted in a military sense, but what is more important to its endurance is its character: an institution created by liberal democracies, with liberal democratic values, that offers protection to its members. Wallace Thies this forward as a simple suggestion: “NATO has become a symbol of what can be accomplished when democracies work together.” According to him, it allows democracies to legitimise their policies at a domestic and international level by highlighting international cooperation surrounding them, allows them to share the burden of military-related endeavours, and gives each of its member states more leverage with the other members. NATO’s expansion policies further suggest it has democratic and liberal values at its core: by expanding to incorporate Eastern European states for little reason besides their democratic nature, NATO is realigning itself from being a military alliance to a more durable political and democratic one. This explanation of NATO’s endurance is very much a Liberal and Constructivist one: by virtue of being an international institution created from liberal democracies, NATO allows itself to endure due to the advantages it provides back to these member states. This makes other democratic states want to join it to attain the same benefits, and allows NATO to grow in ways that help them to maintain their relevance in the world, by unifying a group of culturally and politically similar states.