I'm gonna tell you what I did when I got my first job, it was while I was interviewed, indeed.
When the questions ended I ask them about what 3D CAD, CAE softwares they had and they asked me "what software you recommend us" (I think they were still tested me) and I showed them all the capabilities Autodesk Inventor (since they were using Autocad which is from Autodesk) have. They were impressed, hired me and bought the software.
The first three months I was doing 3D models, renders and drawings of all the equipments they had built for presentation at an exhibition in which they sold $2'500.000 USD in equipments. The following months I was doing design optimization for several machines and structures and later deploying a good manufacturing system, all of that was possible due to the use of the acquired product design suite of Autodesk.
So I think if a company could benefit using certain software (CAD or CAE) they would consider purchasing those software and it depends on one as engineer and end user prove to them the value of investment.
My school taught Solidworks for 3D modeling, CAD and CAE. EES and Matlab for solving a wide range of engineering problems. In addition to that we learn to program in Java in order of not relying on third-party softwares.
I have an interesting experience related to that question.
After year and a half I quit and started to work as independent. One thing I noticed was the time spent on each project and after a while I realized I was overestimating the need for programs to design everything. Then, I started to rely more in mathematical-logical reasoning and common sense and now find that 80% of the projects I can perform by hand perhaps with the help of excel macros and the remaining 20% requires the use of specialized softwares. And I'm more productive now!
I note that many colleagues have become so dependent on the use of CAE that in return they're losing their capacity of analysis, deduction and troubleshooting. And it's something that as I read, it has been observed in other professions where technology increasingly plays a predominant role.
So in response to your question, first I would verify whether the extensive use of such tools is justified, and if so I would recommend the company to acquire those tools as long as the investment is guaranteed. Another thought that I would add is that these softwares should not make one feel more confident but only more productive.
For the last question, I will continue to work as an independent until to get sufficient funds to acquire certain softwares and use them to do things that are entirely on another level.