Doing some assessment internships/internships or working as trainee at some firm could not be riskier than sitting idle and waiting for an opportunity to come at your doorstep. I believe it's better this way. And just imagine if you keep on applying and you still don''t receive any response for a month or two. You could have otherwise used this time to add some experiences in your CV while simultaneously applying for jobs.

In today's market, you will have to reflect it to the recruiter that you are willing to put in all your efforts and even struggle for that matter (by doing internships) till the time you don't receive an offer. Yes, the market has become ruthless. If you want to enter it, start getting your hands dirty as soon as possible.

And you can definitely get an internship converted in offer with cut-throat experience in your interest domain. Just be clear with the partner of the firm that you are here for getting recruited. Humbly ask after/within a month, for the feedback and prospects of working with them. Many law firms and their partners are there to just exploit people. They can ask you to work as assessment intern for 3 months by paying 5k a month. Avoid such firms. They are completely sham.

Don't wait for vacancies to come. Most of the time, firms don't go about posting vacancies info on social media or even on their websites. Instead (and this has become ubiquitous), that they hire interns who perform well and had associated with such firms on long term basis. So apply for assessment internships (or even just internships) at almost all firm. Be it Tier 3, Tier 2 or Tier 1. Market scenarios are not good. It's not necessary that you will get hired by the best people in your interest area. Start with small steps, and try to climb the ladder with experience.