eIDAS was intentionally formulated to allow such signature services, making the whole thing quite pointless from a security perspective.
This method would most likely be eIDAS confidence level low. They (like many other providers) most likely offer multiple LoA variant but only advertise the lowest one online so you think you are "ok" with an easy to use variant but when push comes to shove you need to upgrade to substantial or high, do the full validation scheme and get a QSCD to do you signatures with.
The first "shall not be denied legal effect and admissibility as evidence in legal proceedings solely on the grounds that it is in an electronic form or that it does not meet the requirements for qualified electronic signatures."
Qualified signatures used to require that the private key was physically on some tamperproof chipcard (or similar), but eIDAS changed that. Now, you can rely on some vendor's implementation of cloud signing services that is certified to ensure(?) that "signature creation [data] [is] with a high level of confidence, use[d] under [your] sole control". Much like how many people don't manage the secret keys of their crypto wallets.
For remote QCSD the relevant spec is ETSI EN 419 241‐2 PP. It has very few requirements (8.1.8) about authentication, only that it should be resistant to guessing your PIN/password, and it should only let in the legitimate user.
Note that you can get certified as a qualified trust provider by EY or KPMG.
The decision to require users to use an emailed link to view and sign a message could stem from DLP requirements. Emails are plain-text and therefore any sensitive data leaked could be irreversibly exposed. By keeping the messages inside a system that requires authentication, there is less likelihood that a someone besides the intended recipient will interact with the message. Such systems also support auditability and DLP scanning.