The reinvesting-of-interim-cash-flows-at-IRR (RICFI) assumption is neither required for nor has any impact on the calculation of IRR of a project, or a debt instrument's yield-to-maturity (YTM), IRR's application to debt instruments. I think the Investopedia article you have mentioned is a bit misleading in that respect. If mentioned at all, the RICFI assumption is in essence only a reminder that a "project" with some early cash flows such as a coupon bond is subject to more reinvestment risk than another one with predominantly late cash flows such as a discount bond.
Those trying to match certain liabilities rather towards the end of a project or thinking that interest rates may decline somewhat early in the life of a project may consider a project with front-loaded cash flows as having reinvestment risk. Yet others who might think the interest rates might rise or even better opportunities might come up somewhat early in the life of a project might view such projects as rather presenting reinvestment opportunities and prefer them. If such issues are important for an investor, s/he might consider assessing a project in more depth under different scenarios with more variables but bringing in additional variables and forecasts to an assessment is likely to make it more complicated and may actually reduce its usefulness if not really needed.
If one is trying to decide on one or more limited-life projects with high enough IRRs, computing their durations might help in identifying the level of reinvestment risk/opportunity associated with them. Debt instruments such as bonds are nearly always subject to duration analysis and I am a bit surprised this technique is not used more frequently when analyzing financial aspects of projects with limited lives other than debt instruments.
Addition / further comments
Some of the later answers to the OP seem to suggest that either the RICFI assumption should be included in stating the IRR of a project (or YTM of a debt instrument) or, implicitly, the project’s IRR is recalculated after the use of interim cash flows are explicitly accounted for until the end of a project. This is in general unnecessary and misleading at least for the reasons below.
First, suppose we have two projects providing the same total net cash inflow over the same number of years but one of them provides some of the positive cash flow earlier than the other. According to the time value of money concept, the project with more positive cash flows early in the project should be ranked higher. The IRR equation based on original cash flows ensures this is the case. That is, contrary to one of the claims in one of the answers, the IRR gets realized as “promised” as long as the payments are made on time.
Second, what one does with the interim cash flows is external to a given project. As soon as scenarios on how the interim cash flows might be used are included in the calculation of an IRR, we would be calculating the IRR of a different project. The egregiousness of the focus on the handling of the interim cash flows can be exemplified by thinking about how the interim cash flows should be accounted for if they were to be immediately spent by a person or paid out as dividends by a company. Only an IRR calculation based on original cash flows would account for such events correctly. In addition, if we can assume the spent or distributed interim cash flows have provided the expected returns, then we can safely assume that this is the case for all interim cash flows given a certain project.
As I said before, the RIFCI assumption is in general superfluous. Tools such as duration analysis might be more helpful than a mere “fair warning” statement such as RIFCI if and when actually needed. I think the treatment of interim cash flows should be included in a project’s IRR calculation only if this is critical to the investor in deciding between projects and the use of interim cash flows and their returns can be estimated with some certainty. However, if this is done, one would be calculating the IRR of a different project. More importantly, unless really needed, the project's analysis would likely get more complicated and uncertain without being actually more useful.