I say this as someone who built data infrastructure before and after the invention of data lakes, and I have done it every way - the old and the new.. For the record, for a lot of scenarios, the "old ways" actually do still work fine. But there are new opportunities/possibilities too.
I really understand what you are saying... I know the hype problem, I lived it. It makes me both frustrated and sad - because the hype is annoying, there is a lot of vaporware - but there is also something real that is happening too which is part of the story of the evolution of data architecture/infrastructure. My strong advice is, being open-minded is helpful - learn and take what was good/real and leave behind the stigma/hype. Something real and useful happened in terms of architecture, so take the benefits - but of course, don't compromise on delivering real, working solutions.
Regarding "data lakehouse", I struggle with the buzzword term also, but once again, I recommend looking at what is good/real and ignoring the stigma of the buzzwords. One way of looking at it is the literal translation - a data warehouse made from the components used to make data lakes. To be honest, it is a marketing term, but it is also an architectural pattern we had even before the term existed - for example - you could use a data warehouse product such as Vertica, and back it by HDFS - guess what, there's a data "lakehouse".. and most of the big database vendors can do this trick now - a full traditional data warehouse engine sitting on top of lake storage infrastructure.
There are several "real" use cases for data lakes. Precursor architectures could be seen to be "operational data stores" [1]. Data lakes are real, they are one approach to solving some problems.
These use cases could include: 1) raw, long term storage of large volumes of diversely structured data for staging/historical purposes; 2) data discovery/exploration of this data to identify patterns/models and relationships (this is both an AI and analytics use case for power users and BI/analytics/data scientists, etc.); and 3) an opportunity to change the paradigm of traditional ETL - instead of pulling from sources, one way you look at it is, allowing many diverse/distributed sources to push their data into the lake for powering analytics, exploration, AI model building, etc. It makes sense as part of lambda/kappa architecture as well - some of the "push" in can come from streaming sources as well.
Use case #1 is very much a "data infrastructure" kind of use case that we do anyway in data warehouses - especially those that do ELT (vs. ETL) - staging databases. If you want an architecture that actually helps make some sense of such a use case of data lakes more formally, one could look into Dan Lindstedt's data vault architecture [2]. While data vault modelling doesn't necessarily require "data lakes", the "raw" part of the data vault architecture use case overlaps nicely with data lakes.
[1] https://en.wikipedia.org/wiki/Operational_data_store
[2] https://en.wikipedia.org/wiki/Data_vault_modeling