Isn't obliging the husband to financially support his abusive divorcee until she remarries an injustice to him and an impediment to his responsibilities and new life? And what are the Islamic legal rulings in such a case, and are there any penalties for the wife?

Justice is the foundation of Islamic law. Allah does not wrong people, and He has given everyone their due. It is obligatory to ascertain the truth before objecting to rulings. The Sharia did not obligate the divorcer to spend on his ex-wife until she dies or remarries, and this is not part of Islamic ruling. The financial rights of a divorced woman are limited to: any remaining dowry, maintenance during the iddah (waiting period) only in the case of a revocable divorce, mut'ah (compensatory gift for divorce), and the wages for custody and breastfeeding for young children. Monthly maintenance for a divorced woman until she remarries is not from the law of Allah, but rather from incomplete human legislations. It is not permissible to equate this injustice against the divorcing husband with the legitimate mut'ah intended to console the divorced woman with a specific, reasonable amount, according to the husband's financial situation, whether he is well-off or in straitened circumstances. In summary: a divorced woman is not entitled to any maintenance except in specific cases such as a revocable divorce, pregnancy, or custody.