Some of the firms not at the top of the rankings struggle with vacation schemes. They will get people on them easily but then converting those people on to training contracts can be difficult - sometimes candidates are just using firms to build their CVs rather than truly having a long term ambition to work for the firm. For those firms, they can often choose not to run vacation schemes as they are costly and time consuming. Other firms just don't have the resource to run vacation schemes effectively even if they are getting the right candidates in. Considering they are only taking 8 trainees a year, it could easily be the case their Grad Rec/Grad Development team is very small (possibly not even the equivalent of 1 full-time person) and therefore running a vacation scheme is something that no one has time for.
Either of these reasons could easily be the case for a firm like
Howard Kennedy rather than them feeling like you need more experience. If they wanted to limit applications to a certain group, they would recruit later (e.g. recruit now for 2021 intakes) or say you can only apply as a finalist/graduate. Having had a look at their website, that might be the case though - seems their deadline for 2022 intakes is May 2021, so only finalists, graduates or those on the GDL could apply.