[W]hy hasn't the Ukrainian state joined the North Atlantic Treaty Organisation?
— because of the combination of internal and external factors.
The external factors are discussed in details in existing answers. Let me focus on internal factors that Ukraine has to improve before it could be awarded with the membership (and the absence of which has prevented Ukraine from membership in the past, which is the direct answer to your question).
- reforms in defense sector that would make Armed Forces of Ukraine closer to NATO standards, which, in turn, is a cornerstone of a country's participation in a defense alliance;
- reforms in security sector and combating enemy's espionage. You literally can't be trusted confidential information of a military alliance if your top government positions are controlled by acting officers of the alliance's main adversary;
- To give you an impression of how bad things are after the 2019 elections: for more than two years (2019-2021), the Zelenskiy regime has failed to appoint¹ heads of Ukraine-NATO and Ukraine-EU committees. You can't accomplish anything if your profile committee is effectively paralyzed;
- reforms in economy, decentralization, promoting the rule of law, fighting corruption, eliminating the influence of the oligarchy and foreign-sponsored organized crime;
NATO members recognize (see quote below) that throughout the recent years, Ukraine made a substantial progress making these reforms, it's still a consensus that, as of June 2021, the progress is not sufficient to become a NATO member.
Has NATO ever made open statements on Ukraine joining NATO?
The 2008 Bucharest summit of NATO has paved the way for Ukraine's membership to NATO.
The 2021 Brussels summit has confirmed that decision. I'm placing here the article 69 of the joint Communiqué because it not only answers your question in full, but also defines specific steps Ukraine has to take in order to get ready for the membership (referring "internal factors" from the top of my answer). I took my liberty to split the text into paragraphs for readability.
We reiterate the decision made at the 2008 Bucharest Summit that Ukraine will become a member of the Alliance with the Membership Action Plan (MAP) as an integral part of the process; we reaffirm all elements of that decision, as well as subsequent decisions, including that each partner will be judged on its own merits. We stand firm in our support for Ukraine’s right to decide its own future and foreign policy course free from outside interference.
The Annual National Programmes under the NATO-Ukraine Commission (NUC) remain the mechanism by which Ukraine takes forward the reforms pertaining to its aspiration for NATO membership. Ukraine should make full use of all instruments available under the NUC to reach its objective of implementing NATO principles and standards. The success of wide-ranging, sustainable, and irreversible reforms, including combating corruption, promoting an inclusive political process, and decentralisation reform, based on democratic values, respect for human rights, minorities, and the rule of law, will be crucial in laying the groundwork for a prosperous and peaceful Ukraine.
Further reforms in the security sector, including the reform of the Security Services of Ukraine, are particularly important. We welcome significant reforms already made by Ukraine and strongly encourage further progress in line with Ukraine’s international obligations and commitments.
We will continue to provide practical support to reform in the security and defence sector, including through the Comprehensive Assistance Package. We will also continue to support Ukraine’s efforts to strengthen its resilience against hybrid threats, including through intensifying activities under the NATO-Ukraine Platform on Countering Hybrid Warfare.
We welcome the cooperation between NATO and Ukraine with regard to security in the Black Sea region. The Enhanced Opportunities Partner status granted last year provides further impetus to our already ambitious cooperation and will promote greater interoperability, with the option of more joint exercises, training, and enhanced situational awareness.
Military cooperation and capacity building initiatives between Allies and Ukraine, including the Lithuanian-Polish-Ukrainian Brigade, further reinforce this effort. We highly value Ukraine’s significant contributions to Allied operations, the NATO Response Force, and NATO exercises.
¹) Head of Ukraine Mission to NATO Mr. Georgiy Tolkachov is at the Acting Interim (a.i.) status