Nowadays it's two mediums or a hard at every company paying competitive salaries. Anyone working isn't going to have time nor energy for practicing hundreds of mediums and hards.
Also recently just getting all the questions correct isn't enough anymore. You have to several other people that also solved everything correctly.
Outside of elite finance shops (private equity, HFT, quant shops), unicorns (Uber, Coinbase, Stripe, Airbnb etc) and Netflix that do a lot of gatekeeping, the Hards asked are generally either classics or easier (Levenstein's, median of two sorted arrays, median of data stream, Dijkstra's variations, k-way merge) and more straightforward hards (generally true even for most of Google's problems). For Mediums, it should only take about 200-300 to gain proficiency provided you cover all the primary patterns and data structures.
You are correct about solving it correctly not being sufficient. 1) Interviewers have interviewed hundreds of candidates and are trained to discern those that memorized from those that truly understand. This includes not only justifying why then solution is correct and demonstrating the reasoning to arrive at the solution, but also discussing other possible solutions, the tradeoffs between each one (generally time and memory complexity), and explaining why the solution you choose is optimal. 2) Interviewers assess your ability to communicate effectively, including asking clarifying questions and identifying constraints and preconditions (often interview questions are tweaked from the original LC question) to fully understand requirements, an area where H1bs are at a disadvantage. 3) Interviewers also assess your ability in writing clean code, consider edge cases, and test and walk through your code (does your test cases cover all possible branches, particularly aforementioned edge cases).
Then of course, LeetCode is only sufficient for entry to mid level positions. Anything more senior also has heavy emphasis on system or product/API design as well as behavioral questions and your past experience. LeetCoder memorizers can only go so far, but they do occupy a significant number of the decent but not great software roles in the US.
Finally, majority of companies dont even ask real mediums, many only ask easier/common mediums (ie 3sum, group anagrams, subarray sum k, binary tree pathsum) and easy. You only need a high degree of LC proficiency if you are targeting FAANG, promising/well-backed mid-to-late stage start-ups, and Microsoft and IBM/Oracle type companies. Outside of these companies, being able to solve easys and easier mediums is more than sufficient. Most software engineering jobs are actually with regular (non-tech) companies of varying sizes. There are a few exceptions (ie Walmart's e-commerce technology team likes to cosplay as Amazon), but this generally holds true.
